It depends on what you're wanting to do with the wolf and companion. If you're wanting to grind for money, Isegard's guide suggests 2 furmus + 2 kits for Goldsea 4 (or furmurs + kickstarter krane + 2 kits if you have a krane), or two canictonis + kit + jocol for Icerun 4.
Personally, I like to attach a radiant kuzma to any wolf that I want to level, but haven't gotten around to grinding the campaign for levels just yet. This includes puppies. Kuzma grant XP when played with, and the radiant version can be played with each hour. If I'm diligent, I can get a puppy to level 7-8 by the time they grow up. The kuzma are also decent in Icerun 3 against the lapistrix, because they do a lot of damage and can defeat the lapixstrix before their intersect comes into play.
My personal favorite companion to use is the canictonis for their incredible poison. Fun fact, in Early Access, there was a bug that made it so poison, bleed, and healing effects didn't drop off when they should, and would just stack infinitely. Canictonis, and any poison-dealing companion, was beyond OP. I used them judiciously in campaign, gauntlet, and arena. So I still have some warm feelings towards them from that time, even though the bug has since been squashed.