First off, I would strongly recommend that you read Maya’s Carnival Guide to Pets (linked above by Medea).
That’s the advice I do my best to follow 
That is - your character resists + survivability first, then pet resists + pet damage.
Of course, I am leveling this guy in hardcore mode, so that is extra important.
I got reckless with a character at around level 25-30, and died in a blink of an eye.
If you’re in regular mode, then it’s not nearly as critical.
Now I am leveling a new one, still in hardcore.
He’s level 59 now, and just a few minutes ago I finally took the time to hunt around for the correct augments and components (from factions and from my stash+blacksmith) to try and max out most of my resistances.
As for gear while leveling:
You are on the right track with picking up +pet skills + pet buffs stuff, and of course try to find balance in your own resists so you’re not dying. (ideally items with +pets and +character resists)
Overall though, you’ll likely level with a mix of Monster Infrequents and Faction gear.
For faction gear:
At level 35 (and then 70) you can pick up a good chest + shoulders from Rovers in Old Arkovia. At level 40 they also have an amulet.
At level 65, you get a bunch of faction gear options opening up with +pets skills: mostly from the Forgotten Gods factions.
Around level 90-94, you get some options from Ugdenbog Coven, as well as a few more options from the other factions.
On the Monster Infrequents side, there’s also options all over, these can be “refreshed” every 20-30 levels if you so desire.
At the lower levels, if you happen to get one, don’t worry much about the additional affixes, just roll with it.
As you get higher up in levels, it’s not the worst option to do a couple-three runs at the boss (if it’s a boss MI drop) to get yourself a nice prefix or suffix with even more +pets.
For specific examples (ones I’m currently using):
Ascendant Cowl helmet
Bloodsworn Signet rings
Bloodsworn Codex offhand
Zaria’s pendant
Wendig Gaze medal
Rhowari chest + shoulders (faction items)
And Savage relic (you can craft a Hysteria relic at lvl25 which you can use to then craft Savage).
For the Zaria’s pendant, I killed her a few times to get me a +pets suffix (of the Wilds).
For the other MI’s, they drop quite often, so I naturally got half of them with a +pets prefix or suffix (giving me more +Familiar/hound/briarthorn/support skills)
Edit: What HonorabruSudoku wrote also works
He even got item links in and all.
Overall, the Grim Dawn item database is pretty great for looking up faction gear, monster infrequents, and looking for those augments/components when you try to figure out how to fix your resists 
Edit 2: Oh, and almost forgot, Salazar’s Sovereign Blade is a nice dagger to use as well.
I don’t even use it’s temporary summon. I got one with “of bestial rage”, so it gives me +2 to Familiar skill, +2 Hellhound skill, and the suffix gives +3 Briarthorn skill.