I really need game recording software that suits my needs.

This post is probably pretty common, so I apologize if you've seen this a bazillion times. I just started a YouTube Channel on May the 9th. It's the 15th, and I'm past 200 subs. I couldn't be happier at my growth. But my current game recording computer up until now has been my desktop that I built. And It has some significant grunt to it. I am going to college after this summer, and I won't be able to bring my desktop along. I do however, have a laptop that I am bringing along with. I already use it to piece together the footage from my desktop, and I use it as an audio recording PC. But if I'm going to continue using my YouTube channel in college, I need a game recorder that can run on lower end computers. So ideally it would have to fit these criteria, Effectiveness (Does it work with decent quality), Cost (Please be free), and unobtrusiveness. For the last one, I used to record stuff using Bandicam because it was free, but I started using Plays.tv because it didn't have the watermark. Any recommendations are welcome, thank you for any responses.