I am creating song and need to recording singing through my computer mic, I'm not sure what device to use to accomplish this

Reason can't record audio input, you'lll need to get a DAW and learn about rewire. That way, you can record your vocals on that DAW and keep your beat/instrumentals in sync while you rewire.

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DAW = Digital Audio Workstation which means the whole system including computer, MIDI-controller and a sequencer software, but many people just mean the sequencer software (like Cubase, Reaper, Ableton Live, Fruity Loops) when they say DAW.
Anyway, if you want to record singing, you should really use a sequencer software which can host Reason via Rewire. Rewire is an interface to include one audio application into another and exchange MIDI data and audio data between them.