The shakey screen and video lagginess you get are directly attributable to running in software mode. When you do that you throw all of the work for drawing the screen onto your CPU. When I tried running the game in software mode on my old computer, I got the same sort of problems. A slow laggy video rendering, and lots of missing detail.
Running in D3D or better yet Open GL with that improved renderer (the one that comes with the game sucks) puts your graphic card to work and greatly helps speed up the rate at which your computer can redraw the screen as you move and look around.
Cliffy B has said on his website that UT uses computer resources in the following order of importance:
1) CPU
2) Graphics card
3) RAM
Considering how old the game is now, a 1.3 gig CPU is plenty. Your 32 MB card isn't bad either, I believe it was standard when the game came out, but if you can get a better PCI card then go for it. If you can find some used RAM you might want to go up to 512 MB some day, but as you can see from the list spend your money on the card first.
