Hey! and welcome to the world of "i have a recording studio =D"
Well firstly, it depends what you want to do.
The basics for recording would be.
-Mixer
-Audio Interface (Gives better recording quality)
-Pc or Mac
-Studio Monitors and Headphones
-Multitrack Software ( for recording, mixing and mastering )
-Microphone ( Condenser or Dynamic ) Studios prefer Condenser Mics
-Any other thing, like Keyboard, guitar etc......
To start with, I would suggest that you use "Kristal Audio Engine" for the multitrack software, it's absolutely free and very powerful, especially for a beginner.