The P3-AT is DEFINITELY the sort of gun you would want to keep "one in the pipe". Racking the small, stiff slide can be tricky to do, and if you don't do it just right, the first round can "stick" sometimes. This is not a problem when racking is done automatically by firing a shot (at least in a properly functioning gun) but sometimes, to hand cycle rounds it takes a bit of a special touch.
So, I would really, really advocate not carrying it with an empty chamber for self defense. It has a long enough trigger pull to be safe, IMO, as long as you are safe. Get a good holster, also...another pretty essential safety tool (sticking a loaded pistol loose in your pocket with an exposed trigger is demonstrably less safe). Think of it like a revolver. It took me a while to get comfortable with carrying a round "in the pipe" but especially with a gun this tiny, you do not want to be trying to rack it, fussing with the slide, trying to get that first round to feed properly, when you really need it to just work.
There are guns I prefer an empty chamber in though. My 1911 copy...I know, I know, it really isn't as unsafe as it feels cocked and locked, but I just can't do it, its a mental thing. Same thing with my Saiga shotgun. Just can't bring myself to have a fully cocked hammer poised over a live cartridge, at least not yet.
Anyway, get whichever one you prefer (I prefer the P3-AT) and I think you will like it!