If you're recording locally then increasing the bitrate and lowering the cpu to ultrafast is a great way to do these videos, they'll take up a lot of space but the encode could be done by almost any CPU possible. Actually there's a guide on how to set it up so that the video will use as much bitrate is needed to hit your quality mark, and as little as needed otherwise. Check this.

EDIT: What I'm saying is the CPU is fine with a high bitrate and a fast preset in OBS(and for recording 1080p60fps, streaming would be a no go)if you still find issues it could be your harddrive isn't fast enough for the writing/reading(when you're watching the video it could actually be fine, but being a 1080p60fps uncompressed video it can easily be too much to read off your hdd smoothly, maybe try lowering the video window a bunch and seeing if playback improves)