that amount of stuff,a basic arduino could handle easy.
Best way to start out would probably be grab some LEDs, get them to trigger on and off (these will emulate the relays).
Then grab your sensors, get them to read data, and set up your humidity and temperature points so that when its too dry or whatever, itll turn on the LEDs.
Then grab the pumps and relays, and just replace the LEDs with the relays, and your on your way to a nice thick shiitake stew.
I noticed you mentioned 2 relays though and the LCD, do you need a LCD to be recommended, of have you picked out one you like (because they can become problematic sometimes).
Also whats the second relay for, to trigger the computer power supply off and on to run the fans? Or will there be 2 misting pumps?