First of all, Welcome to TechIMO!
If you're looking for a small PC that you can build yourself
Shuttle sells Small Form Factor (SFF) boxes that are barebones (require you to install CPU, RAM, and drives). I've built these things several time, and they are stable. Although, sometimes it takes little hands to get into certain spaces

You can usually pull one of these for a P4 (they make them for Athlons also) for about $199 (great if you already have some of the hardware components needed).
Also, places like
TigerDirect often have complete systems without an Operating System on them (use a copy of 98 or 2000 that you already have) for about $300-800.
When you're tight on cash, laptops aren't always the greatest way to go...especially if you do a fair amount of gaming. However, if the mobility if more important to you, then check out a used computer store in your area. You can generally find a 800MHz~1GHz machine for around $899.
Hope this helps!