I'm not too strong on the tech front of this wonderful hobby/job/lifestyle, so here goes...Would adding a Voodoo card to my system have a positive effect on Bryce as far as rendering is concerned? Also, where does the power lie during a render? Is it the RAM, the processor, or both? In short, what can I do to speed up render times?

Video cards will help with on-screen drawing only. Processor & real ram are key. There are some tips for smaller, faster files in the tuorial sections (I think).

Render times are going to be slow no matter what you do. A video card will speed up your working time as it speeds up redraw. The more RAM you have, and the better the processor the faster the render will be. You can also use tricks, use backdrops instead of building whole backgrounds. Composite, Render your background, then put it on a 2D plane as a backdrop. Try not to use too many volume of glass textures. It's going to be slow to render no matter what you do. That's just the nature of 3D work

There is a rather obvious solution to speeding up worrking and render time. I bought a second computer. You can get a cheap emachines for $399 with a 533 and 32mb ram I added some ram and for less than $500 I have a machines that renders and lets me work and render.