1.- A Computer. Mac or PC, fairly new.
2.- DAW software. Pro Tools, Cubase, Logic, Nuendo, Digital Performer... The List goes on and on, all sound great and include their respective plug ins, some of them quite good.
3.- Audio interface. Loads of brands and sizes, you need one with 2 inputs, at least 1 pre amp. EDIT: M-Audio makes fine cheap interfaces specifically made for home studios, check their site. Fast Track will work, only $149
4.- Microphone. The best ones for vocals are condensers. A Dynamic will work for a demo, but a condenser will make it shine. My recommendation would be an Audio-Technica 2020: Sounds great and it's $99.
4.1.- Pop Filter. This is BASIC for recording vocals, so you don't hear every spit.
4.2.- Mic Stand. No need to explain.
5.- Headphones. Record with these. If you can't afford Monitor Speakers yet, mix with these.
Everything with all their respective cables and wirings.
This is a most basic setup to get a nice home recording.
About
the Digitech RP-350: I don't think it would be of much use in a hip-hop/rap studio. I would sell it to afford all the other stuff.