Keep in mind that to follow the Persist program, you don't need any equipment at all if you choose the Minimalist track - so if you ever find yourself in a situation where you can't get to the gym, you'll still be able to train with bodyweight. Minimalist also comes with low equipment options where all you need is a set of dumbbells or kettlebells.
For the other tracks, here's a full equipment list broken down into roughly how often each piece is called for - but you can substitute as needed.
Used in most or all workouts (except Minimalist):
Bench
DBs (moderate working set weight & metcons)
KBs (moderate working set weight & metcons) - 50/35# is used for metcons as recommended weight for males/females, but adjust as needed
Pull up bar
Barbell (Perform is the only track with Olympic lifts if you have an Oly bar available)
Weight plates
Bike or rower
Bands if need to assist pull ups or mobility work
Used in some workouts:
Rings
Jump rope
Heavy KBs (>= 70# for carries)
Slantboard (alt option: lift heels on a bumper plate)
Rig or post to hold onto or attach a band to
Bar for dips (alt options: ring or bench)
light DBs
light KBs
Landmine (or simply wedge a barbell with one end on the floor)
Box
Occasionally used:
- GHD (fine to sub with regular sit-ups)
- shorty bands
- wall space for wall walks