The link that PrincessGuard gave is a good one - lots to read and learn there.
You should be able to play a region 3 DVD on your PC, but be aware that the dvd-rom, the dvd software, and the OS have "counters" that count the number of times a region is changed until they lock on a region. For example, many dvd-roms and dvd software (PowerDVD, WinDVD, etc) give you up to 5 changes. Windows XP only gives 1 change I believe - other versions of Windows give more I think. So be careful if you plan to use your PC dvd-rom for multiple regions. To watch different region dvds without changing the counters you'll need to make your system region-free, which can be a hassle. There are several region-free guides on the net that can help. I've heard that a program called Region Killer (I think it somehow bypasses or disables the dvd-rom's counter) is good, but I haven't tried it. A program I've used with good results is DVD Genie which I use to disable/reset the counters in my dvd software (I'm using WinDVD) and my OS (Windows XP). As for my dvd-rom, I bought an old 5x Samsung that is region-free by default because it was made prior to 2000 when the region codes went into effect. Your Pioneer would probably require new firmware - the Region Killer software I mentioned before might be a safer bet.
Bottom line is there is a bunch of information available (do a Google search for region free dvd) and if you do your homework you be ok. Good luck!
RB