You should be able to run it, but it would hover at about 40 or 50 frames at max on GTA V. I think all the other games but arma 3 should be fine. That might be a bit lower on the frames. Not sure.
You could use OBS studio edition. It works well, is easy to use, and its completely free. Also, microphones are hardware and need to be bought not downloaded.
You could always use OBS (Open Broadcasting Software), its free and can be used for video and audio recording. I like to use the studio version and if you don't put an image or recording screen then you can just record audio with a black screen.
A couple of games that I enjoy are Warframe, Overwatch, TF2, Terraria (It's a bit slow in the beginning), Toribash, Starbound, Just Cause 3, Borderlands 2, Don't Starve (Normal or together) just to name a few.
Well, one recommendation that I would have for relaxing music would be https://youtu.be/-_wKk3RIsv8
It's the opening/main theme to one of my favorite video games.