I am new to being a DM and soon will have my first session. Since we are with three players total (me as a DM plus two PC characters) I want to help them out a little. The players are a Dwarf Cleric and a Rogue Halfling (The premade characters of the 5e Starter set)

At first I thought about giving them some more potions/scale the battles but that feels less fun than my other idea. My other idea is creating a wolf companion character.

The party in question is a lvl 1 party. I intent to have this character level with them and have access to barbarian skills like Rage etc. (mostly what would fit a wolf)

I took the basic stats off the default wolf enemy and modified a few things. I increased the intelligence since it is a somewhat more intelligent wolf and it's also a little bit more charismatic.

I will control this wolf for his own actions, but I will allow the players to give commands etc. The end goal is to balance out the party a little bit so they can act more like a party of three (or two and a half)

The sessions will probably be loose regarding the rules (I don't intent to micromanage skills etc) since we just want to have fun of course ;) I intent to take them through Phandelver Mines first, and if it goes well I want to put them straight into the PoTA campaign.

I gave it the following stats:

Race: Wolf

Class: Basically Barbarian without armor/weapon proficiency

Alignment: Neutral

Stats:

• STR: 13 (+1)


• DEX: 15 (+2)


• CON: 12 (+1)


• INT: 7 (−2)


• WIS: 12 (+1)


• CHA: 8 (-1)

Saving throw proficiencies: Strength, Dexterity

Skills:

• +4 Acrobatics


• +3 Athletics


• +1 Intimidation


• +3 Perception


• +4 Stealth


• +3 Survival

Attacks:

• 
  Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: (2d4 + 2) piercing damage. If the target is a creature, it must succeed on a DC 11 Strength saving throw or be knocked prone

Feats:

• Grappler


• Keen Hearing and Smell. The wolf has advantage on Wisdom (Perception) checks that rely on hearing or smell.

I feel as if this thing is either massively overpowered or weak, I am not 100% sure. Does anyone have some tips/guidelines to improve this character?

The term for your wolf is "DMPC" -- a player character that is controlled by the dungeon master.

The risk of using a DMPC is that you might take a lot of the spotlight away from the player characters. The game is meant to be about the characters battling against the monsters and solving the puzzles, and the risk is that it might turn into your DMPC doing all that while the characters watch.

The way to minimize this risk is to minimize the number of decisions that you as Dungeon Master are making for the creature. For example:

• Don't give it any unusual attacks like Grappler, or maybe even trip. Make it a very rules-simple creature that can take its turn quickly so you can give attention back to the player characters.


• Don't make it physically very dangerous, so that the player characters are clearly more powerful.


• Don't give it abilities that would let it solve problems for the PCs. For example, either don't give it good perception skills, or don't have it use those perception skills to notice things unless the PCs ask for that specifically.


• Don't control the wolf yourself. Give the player characters the wolf -- maybe give them a wolf each, for balance -- and let them move the wolf on their turn, just before their own action.

Of course you can choose not to do some of these things. Just be aware that you could be taking the spotlight away from the PCs, which might make the game less fun for them.

As to power: this wolf is weaker than a player character, and that's appropriate. The problem is, even if you give your group two of them, they still won't be comparable to a group made of four player characters, which is what the adventure expects.

To compensate, you will need to weaken the monsters somewhat -- by decreasing the monster numbers, hit points, or damage output in each encounter.

It's appropriate to have the wolf gain power as the group levels, to make sure it stays relevant.

The Frame Challenge

As Mike mentioned, it does not seem like the best way to solve your problem ("my party only has two PCs") is creating this DM/GMPC. Instead, I would recommend just re-balancing the encounters so they are an usual challenge for a two-PCs party. As mentioned in the other answers, a DMPC is usually created for fulfilling something the party can't do, e.g. a cleric for a party without any healing methods. The Wolf seems to only be able to Tank and do Damage, and that is something any party composition can do as long as the encounters are well balanced for that party.

Additionally, DMPCs usually require some experience from the DM and the players to play them without overshadowing the PCs. I do not recommend playing one as a new DM, tbh. You can check some threads about the problems that DMPC'ing usually bring, e.g. metagaming. That's why people usually recommend not making them.

In particular, check this question: How can I tweak the Lost Mine of Phandelver for only 2 player characters? - seems quite similar to your own original problem.

The Actual Question

Compared to a well-built level 1 character, the wolf is really, really weak.

You did not post the HP and AC, so I assume you are using the default - AC 13 and HP 11. With a con modifier of +1, this is essentially a low-armored Fighter or Ranger.

The +4 to hit is lower than the usual for 1st levels for their main attack, which would be +5, and the average damage on hit, 7, is lower than the usual martial attack of 1d8 + 3, which would be 7.5 average.

The Grappler feat is incredibly weak and the Keen Senses feature is not enough to match most of the racial features a normal PC would get.

More importantly, due to low HP and low AC, mixed with being a melee character, I would expect his DMPC to be constantly in the ground unconscious against any reasonable encounter. This means it would probably end up being a resource sink (for healing potions and healing spells) rather than actually helping your party. For example, in the first encounter of LMoP - Goblin Arrows, in the Ambush - I would not be surprised if your DMPC ended up dead, if you decided to not follow the book recommendations of not killing the party.

TL;DR: I think this DMPC will be a nuisance more than a helping hand for the party, and that added to the general recommendation of not making DMPCs, you should consider thinking of other ways to solve your actual problem, which is, from my point of view, running LMoP with only two PCs, which is approached in some other questions in our site, e.g. I'm DMing for a party of two. How can I make sure my players have classes that can play well together?.

Generally, GMPCs are useful for if there is a specific role that the PCs cannot (or do not want to) fulfill, or as a plot device, or as an in-game medium for conveying information to the players (such as a guide or expert). Otherwise, introducing a GMPC has its risks and downsides too.

• As Dan B said, the GMPC should not outshine the players or take the focus away from them. Players get bored if the NPCs solve everything.




• Combats become slower because of the new creature, especially when that creature regularly causes multiple rolls (e.g. attack roll, then Strength saving throw) or grapples.




• Out of combat, the additional traveling companion will take up space and resources. In stealth and social scenarios, the wolf may be a liability.

In terms of balance, your custom barbarian-wolf-hybrid creature is stronger than a wolf, but less effective than a typical melee PC of equal level. Your wolf has relatively low Strength and Constitution, which are key ability scores for the barbarian class. It will also run into some odd interactions between the barbarian class features and the wolf features.

• As 1st level barbarian, it has 13 HP (12 + 1 CON), whereas normal wolves have 11. This is good for a 1st level character, but will be weaker at later levels due to the low CON modifier.




• It's ambiguous whether your wolf uses Unarmored Defense or Natural Armor, but either way it currently has 13 AC. That's very low for a melee character.




• Your wolf currently uses its DEX modifier for attack and damage bonuses. To get the extra damage from Rage, it would need to attack using STR instead, but that would mean its attack rolls have a smaller bonus.




• The wolf's speed is not specified. The wolf stat block has 40 ft move speed, and 5th level barbarians get +10 ft speed from Fast Movement. Will it get both?

As the PCs gain levels, their survivability and combat effectiveness will improve, making the GMPC ally increasingly redundant. If you want to include a wolf GMPC to assist with low level fights, then you may as well give it normal wolf stats. No barbarian features, no leveling up.

Or, instead of a GMPC ally, it may be better to simply adjust the challenge difficulty. This could mean lowering skill check DCs, using fewer enemies per encounter, or substituting strong enemies with weaker ones. Maybe add some environmental objects that could benefit the PCs, such as crates or rocks that PCs can use as partial cover.

Another alternative for improving the party (rather than reducing the challenges) is to give the PCs themselves some extra utility or resources. For example, early in the adventure, perhaps the PCs discover some potions or even some low-power magic items; the Dungeon Masters Guide and Xanathar's Guide to Everything have some helpful lists of such items.

Remember: Focusing the gameplay on the PCs and their choices is usually more engaging and fun for the players. Sharing the spotlight with a GMPC is less so.

Figure out its role, build to purpose

The balance of any game element depends on its purpose. Compared to a player character, the wolf is rather weak, especially a few levels in, but then again it's not supposed to do all the things a player character does. Your PCs should be the ones that solve riddles, come up with strategies and land the final blow on the big bad monster. The wolf is just there to make combat easier.

Going by the class you chose for it - in order to keep spotlight on the PCs, the wolf should mostly act as a buffer to prevent them from getting overwhelmed in an encounter and, assuming the party lacks this role, serve as a vessel for their buff spells. Have it charge at the enemies, draw fire and keep one or two of them busy while the players properly deal with the rest.

In this role, I'd keep its offensive stats as they are but increase HP and AC considerably so it can hold off multiple attackers without the PCs having to rescue it every other encounter. Let the PCs worry about themselves first. Grappling might help keep opponents occupied as well. Yes, it means extra die rolls, but you stated that you're gonna "be loose regarding the rules", so I don't see a problem with handwaving those should they start to become a distraction.

It's still an animal

An important difference between your wolf and most DMPCs is that it can't talk*, and I'd recommend to embrace that. It can't relay complex information, it doesn't particularly care about the plot, it might just wander off in scenes where it's not needed. No point in sending it ahead to scout if it can't tell you what it found. It might be able to smell that buried treasure, but what's treasure to a wolf? In short, you have a great "excuse" to play dumb and avoid metagaming by getting into this mindset.

It's also a pack animal, but certainly not the alpha of this pack. Have it follow the PCs' lead, support, but don't take the initiative. A player's trying to intimidate the goblins? Have it growl at them and give advantage to the player.

*if the party has a druid or ranger, while there's a chance for good roleplay, there's also the - much bigger - risk of the players constantly extracting information from the wolf. At that point, consider giving control over to the players entirely to avoid unintentional metagaming and spotlight hogging.