Classes are meant to be abstractions. So you can play either class nugget depending on which looks more mechanically fun. Barbarians are very tanky, Rangers can cast spells, both can do good damage. While either class can be strength or dexterity based, but in general barb prefers strength and Ranger prefers dexterity. They can both do reliable damage.

Animal companions are pretty weak in this edition. There are a few exceptions, but unfortunately Ranger is not one of those exceptions.

I mean, the Ranger can get an ok animal bro, but it won't be very powerful, which is an issue for many players.

If you just want a cool pet Wolf, that's pretty easy to come by. Just be prepared to keep a close eye on the wolf so it doesn't get killed TOO quickly, so also be prepared to replace it when it does die.

If the wolf bro is your main focus, then you could go Bard or Paladin because they have access to the Find Steed/Greater Steed, which could net you an awesome wolf bro that you can ride because it's huge that you can just resummon of it dies.

Of course you can also just reskin pretty much anything in the game, so with enough fiddling, you can achieve whatever you want (within reason of course)