Lemme help you out a bit. I know exactly the info you want - people who know alot more kind take things for granted, making the answers less helpfull to newer people.
Here is the basic anatomy of a studio. In order of signal path
1. Mics (for vocals, drums, or micing guitar amps)
2. mic pre amps
3. Mixing board
4. Processing equipment (main parts are compressor+gate, EQ, limiter, pre amps)
5. computer for recording and editing (also some fx if you want)
6. listening device (monitors or headphones)
That's the basics. The sound could also go into the mixing board, back out to processing and back into the mixer if your mixer is your recorder.
Obvious you need mics, mixing board, recorder, and listening the MOST
After that I would go with a main pre amp before the mic preamps. after main pre amp go with perhaps a multi fx that has compression limiting and gate and EQ all in one)
Then i would go for the mic pre amp since it's important although it may not sound like it.
That's the BASICS of a studio.