Low Cost Realm
If you are going to record on computer, Go to the Line 6 website and look at the "TonePort UX2 " for your "mixer" selling at about $199. It comes with Ableton Live Lite recording software and has a nice selection of some modeled hi-priced mic-preamps including API, Avalon, Neve, etc as well as a model of the well known
LA-2A Compressor . There are a lot decent inexpensive mics in the "up to $200" limit. You'll get as many opinions here as there are available mics. CAD M179, Studio Projects C1, RODE NT1, ADK A-51S DLX, sE Electronics M1C,
Audio Technica AT-3035 are some ood ones in the upper ranges ($169-199). There are some decent ones for less such as the MXL V67, or the Studio Projects B1, or
the Audio Technica AT-2020, but if it were me..................
Consider touching base with Warren Dent at Front End Audio as he sells this stuff and is a frequent flyer on this forum. Very knowledgeable and very helpful.
In regards to the comments above, there have been quite a few threads that have indeed discussed this topic many times over.
Use the "Search" Function and type in "Rap Mic" or whatever keywords that you feel will get you in the right direction and you'll most likely be directed to many threads.