The only thing that is essential to play Skull & Shackles is the Adventure Path books themselves (in either print or PDF) and a couple of sets of dice. For longterm investment you'll want to pickup a copy of the Pathfinder Core Rulebook, but when you're just getting started the d20pfsrd or Paizo's own PRD are just fine.
If you're planning on running it then having 3 (active) players is enough, but the APs are generally designed for a group of 4, having 3 is a slight handicap but you can help them out by either giving the players a slightly higher point-buy at the start or running a DM-PC to help them out (and the AP has a number of them available from the start). Get them started by directing them to download a copy of the Skull & Shackles Player's Guide and I highly suggest running character generation as a group to get an idea of what kind of party you'll have on your hand. Miniatures are in no way required for this game and it can all be run through the power of imagination, though the miniatures help out a bit.
If you want to just run the campaign as written you'll be just fine but there are a number of additional products that you can get that will help enhance it:
* Pathfinder Player Companion - Pirates of the Inner Seas
* Pathfinder Campaign Setting - Isles of the Shackles
* Islands of Plunder series of mini-adventures from Legendary Games (they slot right in)
* Pathfinder Module - Plunder & Peril (when it comes out)
After that, check out the various threads here in the forums for advice on tweaking the campaign or adding stuff to it.