homemade pop filter would be the cheapest option for that budget, Pantyhose and wooden circle would do the trick. Shure SM58 is an industry standard, although for strictly recording a condenser microphone would be a wiser choice, would need a source of phantom power for that as well (48v required to power the microphone). Large condenser vs. small condenser would be dictated what you are generally planning to record and I am not an expert at which would serve a better purpose. Then you would need an audio interface, I use
the NAtive instruments komplete audio 6, it does the job not amazing, heard some things about the scarlett, seems affordable. You'll need to decide how many instruments/mics you'll be recording at a time, most affordable interfaces come with 2 inputs but you can definitely get one's with more. So a list to summarize:
-Mic: Shure sm58 (dynamic usually on stage, would save phantom power cost and possible to record)
-pantyhose
-wooden circle (those sewing circles would work, not sure what they are called)
-Audio interface (Usb or firewire-firewire would save a slot if short on USB ports, decide how many instruments will be recorded at a time)
-DAW (something free like audacity would work and keep you in budget)
-Closed back headphones (personally senheiser fan here, I have HD380 pro I enjoy)
-Cables (XLR wise choice, lots of interfaces have 1/4" TLR input/outputs)
Monitors would be nice but put you way over budget