The choice of microphone boils down to how far away from the computer you can get. A USB microphone can be delightful, but you can never separate yourself from the computer by more than one USB cable. Noisy computers need not apply.
This is a reasonable, cheap USB desk microphone I was able to get to work with Mac Audacity.
It’s noise cancelling, so you can use it in a slightly noisy room, but the fidelity isn’t perfect because of that. You wouldn’t be happy singing into it. That’s for one announcer
From there it’s basic editing.
You can pause an Audacity recording at any time by pressing Pause. Pause again to resume. Don’t worry about making mistakes or recording too much. You can cut and edit the final recording to tighten it up.
A common newbie mistake is to try to “record a single live perfect performance.” Nobody does that. The idea behind editor software is to assemble the show from shards and fragments. Record the first five minutes before lunch and the last five minutes after. When you get done cutting it together, nobody can tell you had a bologna and mayonnaise sandwich in the middle.
To create a Music CD, Export the performance as WAV (Audacity doesn’t Save sound files), drop the resulting WAV sound file into your burning/authoring program and burn. iTunes will certainly do this and I think Windows Media will, too. Most Windows People opt for separate software. Almost all Mac people use iTunes.
You will run into competing requirements. The faster you burn the CD the more likely it is to fail, but nobody wants to wait until your CD drive gets done clicking and whirring. Never let a PC go to maximum speed. That will almost certainly create beer mats instead of Music CDs.
Use high quality blanks. I use Sony CD-R blanks (Office Depot, Staples). I have not created a beer mat in years.