Some programs will provide you with a PDA (GW is the only one that I know of that provides one for medicine residents). For those that don't, I'd just go with a palm OS with as much internal memory as possible (at least 16 mb). I found that Sony Clie's offered the most power for your buck, but I don't know if that's changed recently. I'd also reccomend purchasing one that runs on black and white to conserve battery power.
The University of Minnesota gives each new resident the Palm Zire 71 (the blue one with the camera).
As far as buying your own, it really depends on how much you care about extra features (or if it's for work only). Most medical reference/calculator programs are really basic, and don't require a fast processor or color screen. Some programs, like the 5mcc series on Skyscape, incorporate color pictures, though, and you will get no benefit from a monochrome screen. Some residents like to have a PDA with a camera so that they can take pictures of exam findings at the bedside and share them during case presentations. If you want to do this (and the institution allows it), you will want a better, faster model (Palm Zire 71 or Sony Clie models).
I own a PalmOS PDA myself, and have no experience with PocketPC PDAs, so I can't comment on those. I hope this helps.