You don't really NEED anything to start paleo except a good understanding of the principles, and a bit of time to find good food and learn to cook it.
When you're ready to start replacing things, though, this list was gleaned from having done a 2 month x-country road trip in 2 packs (on a motorbike), and it's where we recommend starting from, when you're ready to get your home into the game along with your head and body:
- Cast iron dutch oven w/ skillet cover OR 2 Cast iron skillets
- 3 wooden spoons (one with spatulate top)
- silicone spatula
- 10 qt stock pot (enameled or stainless steel)
- Good set of knives (particularly butcher's and paring)
- Reliable source of cooking heat
- cloth bag(s) for collecting food, greens, etc. (or for shopping at convenient farmer's markets in the area)
Body -- everything you need to do you can do with the body you've got. If you're gonna wear shoes, make sure you've got good ones, though -- injuries will NOT help your fitness program. (I'm a fool for my Vibrams and Zems)
These suited us, and we figured out that the rest were just bonuses--not that bonuses don't make things a LOT easier, but from an ancestrally-minded perspective, we need a lot less than we think we do.