Serious Sam - Pros: Huge worlds. Scripting language is rumored to be fairly easy to grasp. Nice algortihmic water effects - nice underwater lighting effects. Con: Lighting can be a royal pain to get right. Architectural tools tend to encourage blocky design.
Unreal Tournament - Pros: Decent lighting. Easy editor. Particle code can be whipped up fairly quickly - in fact, I know someone who did particle code. Nice algorithmic water effects. Con: BSP errors (in Unreal Tournament engine - not in the new engine, heh - more on that later). Very fine lighting is very difficult. No radiosity in lighting.
Tribes2/V12 - Pros: Terrain. Cons: Dynamix closed down - no real "support" should you go full blast at it (with Tribes2 engine at least). Also, better engines available, IMO. :)
Quake3 - Pros: Beautiful static (no dynamic) lighting, plus, true lighting radioisty. Textures look better in engine than Unreal Tournament. Cons: No transparent textures. Editor (QERadiant/GTKRadiant) is a bit harder to grasp than UnrealEd.
LithTech - Pros: Supports terrain - good support from Monolith. Cons: Better engines available, IMO. I've used LithTech, and I don't like it much.
If I were you, I'd probably start the demo in either Unreal Tournament or Quake3, then move to Unreal Warfare if you get funding (Warfare supports lots of particle effects, and other nifty things that Epic probably doesn't want me talking about). The model effects are absolutely top notch, and terrain creation/tweaking (should you use it) is completely ingrained within the editor. However, maps between Unreal Tournament and the new Unreal Warfare engine are not compatible, so plan on scrapping your old stuff unless your coder can write a conversion program (or, if Epic does).
"But you [AmberEyes] have never admitted defeat your entire life, so why should you start now. It seems the only perfect human being since Jesus Christ himself is in our presence." -my Uncle Dean