I use Bandicam as my primary recording software. I also use OBS at times which is a perfectly fine, free alternative. I prefer Bandicam because of the simple interface and ease of setup, but OBS offers more versatility - especially if you want fancy screen elements while recording (instead of adding in post). Bandicam does not stream, it only records.
If money isn't an issue, you'll probably be happy with Bandicam; however, if you don't need to make the investment right now, OBS or even your graphics card software (GeForce Experience for Nvidia, Raptr [I think?] for ATI) should do all you need).