Set a budget.
Cheap = poor quality. Better to get better quality, value, and look for less expensive.
Any mic can record. What the mic plugs into it important. Mics suitable for recording a vocal performance are typically handheld, "dynamic" mics. Wired mics are typically least expensive when compared to wireless, headset-type, or large-diaphragm studio-type mics. For this response, we'll skip clip-on (lavalier), boundary, shotgun, stereo, and any mic not typically used for vocal performances.
Some "recording mics" are used in live performances when the live performance is recorded. The Shure SM58 comes in wired and wireless versions. Sennheiser, AudioTechnica Electrovoice and several others make these sorts of mics, too. These can also be used in a studio.
Some "recording mics" are used specifically in a studio. Large diaphragm mics with a pop-guard are common. Blue, Audio Technica, Rode, MXL and many others make these.
The standard connectors used to connect the mic to the recording device are XLR. Sometimes they are 1/4 inch TRS connectors. Low-end mics in this area would use a regular 1/4" connector (no ground/shield). Sometimes they use USB.
So... step 1, set a budget.
BestBuy has low end mics. Guitar Center, Musician's Friend, B&H Photo & Video and several other music/electronics supply stores have quality stuff for sale. You get what you pay for.