Use OBS, it has the ability to record locally and is the most versatile broadcasting software currently available. You can easily choose frame rate, resolution, video bit rate, audio bit rate, and fine tune all of those settings.
Always remember that frame rate increases your bit rate quickly. 30 FPS @ 1080p is probably somewhere around 3000-3500 kbit/s while 60 FPS @ 1080p is over 6000 kbit/s. It sometimes is beneficial to even lower the quality to 720p just for the sake of lowering the amount of artifacts created on lower bit rates (60 FPS @ 720p is 5000 kbit/s, 17% lower than 1080p).
Someday I will do a tutorial on all this stuff.