Torchlight 2 Must have mods?

There's one called endless dungeon (or something). Can be good if you're having trouble getting through a section that's too hard. I used it to level up a bit and then go back to the real game when that happened

SynergiesMOD, almost the only mod you need.

I dont like modding my games :(

Synergies + TL2 essentials (it's a merge mod, with some small mods bundled together) + Awesome Classes Reborn (adds some nice fully developed classes) install those, they are compatible with each other, and the workshop make everything easier (even auto-patch)
also this for some good and kinda lore friendly new weapons

Armorless Mod
http://steamcommunity.com/sharedfiles/filedetails/?id=138559525

Human Followers (v.13)
http://steamcommunity.com/sharedfiles/filedetails/?id=138876271

Finished the vanilla version without any problems...

synergy

What kind of mod would you recommend for being able to change out pets to any kind of animal we want at any time?

The devs made a few unofficial mods that you can find, they're pretty much the top mods on workshop. Extra chunky is one and there's a couple of others, they're fairly close to "DLC" but free obviously.

Diablo 2 Music Mod