If you're looking for a "go buy this microphone" answer, I'm not the guy...
Minimum to start is an audio interface, boom mic stand, microphone, popscreen, headphones, and mixing software (DAW). IMO this is a challenge at your budget, but maybe you have some of the pieces already.
The least expensive audio interfaces out there right now seem to be the Behringer U-Phoria line. I have no experience with them. They do come with a license (after product registration) for the Traction DAW, something else I don't have experience with, but you can search around and see how people like the particular interface that fits your budget and how they feel about Traction software. (Most interfaces come with a DAW of some type, often a "lite" version, but probably enough to do what you are planning.)
I would simply work up a budget and see how much you really have left for a microphone, once you have everything else you need. Then, read reviews and narrow it down to a few, and then ask around for experience with the models you are looking at. I will say that condenser microphones are often better suited for the low cost interfaces, so those might be what you need to start with. (The guy at therecordingrevolution.com recommends the Samson C01 in his $350 home studio setup, and the video says it's only $79, FWIW. Again, no experience.)