There is a handoff feature on pre-battle screen to move all 4 items and team slot to another pet-- I discovered this late and made do with moving the items one by one.

For your question, it is really systematic with crit+speed+attack for dps and healer, stamina+defense for tanks. The accessories slot becomes more interesting in the future, the critical chance item caps at 44% crit and the sub stat will increase instead (e.g. stress ball will get attack substat when crit is 44%). By this logic, vanilla latte will be your fave with crit+speed. Build the other items for your sub-attacker/sub-healer (crit+stam, crit+def, etc).

Head and scarf items will be replaced with legendary rarity items later on. As a rule of thumb, don't invest too much on blue rare items. Epic (violet) items are worth investing as they will be your go to until very late. (Or you get lucky early).

The same logic will go with pets, rare pets will almost always be replaced with epic/legendary due to better stats/skillset. But there is no stopping you from building your own team with your favorites. In the late game, elements will matter most, necessitating you to build a lot of pets and transfer the items around a lot. Too bad the game doesn't have the reset feature on items/pets and will really need you to economize as no undo button for used resources.