Depends on what you plan to use pup for but definately get af+3 feet/atleast af+1 hands and relic body/emp body if nothing else
This ^^
- Relic Body is essential for Overdrive duration (though you don't need +3 for that), and a fabulous pet DD or hybrid master/pet DD piece.
- AF hands/Empy body for manuevers
- AF feet for repair
Other stuff is more niche:
- AF body/Relic hands: WSD pieces, but PUP's main WS aren't single hit WSD-oriented weapon skills. Still solid acc/atk/STR though, so they're
good for Stringing Pummel, Victory Smite, Howling Fist even if not BiS
- Relic legs/feet are pet nuking pieces
- Empy head for pet TP bonus (pet only fights)