I am wondering what the best equipment available is.
I want to equip all my battle pets with the best equipment I can.
I plan to have the following parties:
1 Party of pets capped at level 25.
1 Party of pets capped at level 50.
1 Party of pets capped at the max.
This will obviously expand as Sylestia grows, but I would like what's best for right now.

I also want to set up my 3 sets of mission pets with their best possible equipment.
So, if anyone can give me a list I will love you forever!

I don't have a list, but, I do know that presently, the best gear you can get is anything of the Mythical (red) rarity.

Nightfall Bandit Dungeon's bosses have a rare chance of dropping level 25 Mythical gear, and the Dungeon of the Forsaken's bosses likewise for level 50 Mythical gear. As far as I know, level 50 gear is the best you can get, there's no higher leveled gear available, so that gear will be for both your level 50 capped and max capped teams.

As for mission pets, I just max out their stats and pin on the legendary or epic equips that best suits them.

From what it seems, as long as the recommended stat is high (ie lvl50 missions = 780s+), then it's assured to a certain extent that they'll achieve 2 satchels. o:

But yeah, the "best" equips so far are mythicals, only in dungeons.