.NET is compiled language so you cannot "compile" just some classes. But you can precompile whole site after you add some files, that can speed up "cold start", so it would not need to be precompiled on first visit. If you're using "Publish" tool in VS, you can add Post build event which calls precompiler on published location. You will always experience longer start time on first access, you cannot avoid that. At least I don't know how...
Second option is ngen.exe, which will create native image from your IL-based .net managed code, and reduce startup time (on first request, .net will see this native image and just execute it). But with using ngen.exe you are loosing some runtime optimization, because ngen must "play safe", so SSE and similar optimization are not possible. It is recommended to perform performance profiling on using ngen.exe, in some cases app will perform slower!