From the first menu, select SETUP, then GAME OPTIONS. You'll see:

Crosshair +
Simple Items Off
Marks on Walls On
Ejecting Brass On
Dynamic Lights On
Identify Target On
High Quality Sky On
Sync Every Frame Off
Force Player Models Off

Most of these options have an effect on speed. Those that don't are Crosshair, which lets you choose the crosshair to use, and Identify Target, which shows who you are shooting at (can't imagine why you wouldn't want to know). The other options are shown below with the suggested option selected.

Simple Items Off

Turn this to on to get rid of the fancy 3d, bouncing, translucent weapons and ammo packs. They will be replaced with 2d icons of each weapon. The rocket will be a little rocket icon, the rocket ammo is a little rocket with a box around it, and so on. Speeds up the game quite a bit and you get used to it pretty quickly.

Marks on Walls Off

When you shoot, the weapon blast shows up on the wall for a little while (around 4 seconds). You get a minor speedup when you shut this off. Again, the option really adds to the atmosphere, but if you can't spare it, you don't really need it.

Ejecting Brass Off

When you shoot the machine gun or super shotgun, it shows the shell flying out of the gun. The takes time to draw and obscures you view. You won't miss it when it's gone and it speeds it up to turn it off.

Dynamic Lights Off

Whenever you shoot a rocket or the Plasma Gun, for example, it gives off a light, which moves with the projectile. That's dynamic lighting. It involves another texture pass for most objects and slows things down. It looks cool, though. Doesn't add to the basic gameplay, though.

High Quality Sky Off

Pretty self-explanatory. Faster if you turn it off. How often do you look at the sky while playing anyway?

Sync Every Frame Off

Tries to syncronize the redraw with the refresh of the card. This means that QIII may not draw for a 1/60 of a second while it waits for the next card cycle (I think). Leave it off to draw as soon as possible. Turned on only if there are visual artifacts like tearing at the edges of the screen (troubleshooting tool).

Force Player Models On

This is a big tradeoff and the last one to go, as far as I'm concerned. Under the current vertex-animation scheme in QIII, each model takes 2Mb of memory. This option forces all models to the same one (Sarge, the default). The possible effect on speed is that it may allow less paging to the hard disk for memory. If you don't have this problem, then leave it off. It looks cooler to see different characters.