So I just bought and installed Unreal GOTY Edition but the game appears to be lagging somehow. It runs fine, but at like 80% speed, then every 30 seconds or so everything will go ridiculously fast. I've messed with the game speed options and all kinds of graphics settings but nothing seems to work. Any help would be appreciated.

I'm assume you mean Unreal Tournament GOTY and not Unreal Gold.

Anyway it sounds like you have a very high frame rate thats making it unplayable.

Which renderer are you using. I haven't actually tried the GOG version of UT or Unreal so I'm not sure which renderers they include I would use OpenGL or Directx3D8/9/10 but not Directx3D or Software or 3dfx Glide or S3 Metal.

In UnrealTournament.ini
under [OpenGLDrv.OpenGLRenderDevice]

I have FrameRateLimit=62 which would fix your problem I expect.

Under [D3D10Drv.D3D10RenderDevice]

I have FPSLimit=100 which can also fix your problem