Hi there!

I can't say much because I'm not an expert, but I can direct you to some resources that might be helpful! Here's a guide to equipment, although it's rather old. Still, it's useful for early game, non Lost Grove content. Another guide that would be worth checking out is the battler's guide to proficiencies and elements, though that's more battle focused and less on equipment - it does have quite a bit on equipment regardless.

Most armors can be found from loots or satchels, there are a few for sale in the senctuary of saerielle and of course you can have to craft the stoneweaver sets yourself (or buy them from others players). This guide explain all of the elements and accessory in dept if you are looking for somthing a bit more specific. ^-^

https://www.sylestia.com/forums/?thread=45988

equips that you'd use can be broken into four main types based on the stats they give

The main ones you'll see are (one non-LG type, two LG types for lv60+ pets)

Str/Agi- Assassin, Tidal Lord, Warden
Str/Dex- Myrmidon, Storm Caller
Int/Agi- Illusionist, Lightbringer, Reaver
Int/Dex- Evoker, Pyromancer
*

How to pick what to equip your pet with questions to ask yourself:

Is the pet a Magical or Physical element?
> Light, Fire, and Shadow are Magical elements, and get Int-based equips
> Water, Earth, and Air are Physical elements, and get Str-based equips.

What Job does this pet have on the party? Will it be likely to be doing any Tanking?
> Typically the pet that goes in slot one- generally an Earth, Water, or Shadow Tank, sometimes a Light pet- is your Tank pet, and will be taking the most damage since that's where enemies aim the most.
> Tank pets get Agi-based equips, for the boosts to their Mitigation/Defense and their Evasion
> Attackers get Dex-based equips, for the boosts to their Accuracy and Critical Hit rate
> Healers and Buffers generally also get Dex equips but can mix in Agi if desired

(> remember that despite one of the stats being called 'agility', both it and dexterity equally share control of the speed stat. 300 in one and 100 in the other is the same total speed as 200 in both)


example:
Water tank gets
> Water is Physical, so Str
> Tank needs evasion and defense, so Agi
> pet is under lv60, so can't equip LG gear**
> Pet will get: Assassin gear

(**obviously pets over lv60 can equip non-lg gear, but lg gear is just. far superior to non-lg gear, so there's no reason not to go for lg gear and not look back after lv60)

(*Tidal Lord gives more Strength, followed by Agility, Warden gives more Agility, followed by Strength,
Lightbringer gives more Intelligence, followed by Agility, Reaver gives more Agility, followed by Intelligence)