The Dimension 8300 uses a socket 478, 800fsb capable mobo, with 4 ram slots, supporting PC3200 DDR ram, dual channel mode, and an 8x AGP slot.
Sir, you can use any aftermarket PSU that you deem worthy. The only problem being that you will have to cut a hole in the case to allow for installation of PSUs that have a power switch. Alternatively, you could simply search for a PSU that lacks the power switch to avoid this problem.
If I remember right an 8800 GTS 320 MB needs 26 amps, and an x1950xt needs 30 amps. They're both PCI-E, which means a new motherboard is needed. That means a new CPU (AM2 or socket 775) is needed too.
These cards need a dual-core CPU to work best anyway. Recent mobos need DDR2 RAM, so that would need to be replaced too. I think we're looking at a CPU/PSU/MB/RAM/Video card upgrade here, not just PSU
That is, you can't really make meaningful upgrades to that PC, you just need a new one.
Edit: there is an x1950xt AGP, that's as far as AGP goes AFAIK. However, it won't work so well with that CPU. Sorry