Software alone isn't always the solution, recording is extremely hardware intensive, and it's possible your computer isn't up to it.
I doubt you can record at 60FPS, 30 should be possible, but 1080p might not be for your computer.
here's a guide to setup OBS for local recordings, start at the recommended crf 15, and lower the number for higher quality and higher file size recordings, or raise it for slightly lower quality and smaller file sizes.
https://obsproject.com/forum/resources/how-to-make-high-quality-local-recordings.16/
Recording is EXTREMELY heavy on your CPU, RAM and HDD. If you're playing a game that is heavy on any of those (like say ARMA) then you won't be able to record.
You'll have to adjust ALOT of game settings to find the right balance.
Having only 1 hard drive will also be a serious downer because writing a video file is a lot of work and doesn't leave the hard drive much room to breath for reading new data.
Your computer is perfectly fine for playing games, but recording gameplay is an entirely different story, there's no easy "just run this program" solution, you'll have to work to find the right settings to record each individual game as they all interact with the computer differently.
Like my computer recorded every game just fine until I tried to record The Division, and i found out I couldn't record it an FPS higher than 30, even though all my other games recorded perfectly fine at 60.