The OP absolutely has a choice. With his rig, he has available as encoder:
x264 (but the i3 isn't powerful enough to support it)
quicksync (low streaming quality, recording quality as high as you want)
nvenc (good streaming quality, recording quality as high as you want)
For streaming, you must choose an appropriate resolution.
For recording, you record at the native game resolution.
Streaming resolution depends on available upload bandwidth and streaming service. Common service is Twitch, which supports maximum of 3500 for non-partnered streams. 1280x720 at 30 fps is usually bitrate 2000-3500, depends on actual footage. 1280x720 at 60 fps needs minimum of 3500 bps, but usually looks worse than 30 fps if given too low bandwidth. 1920x1080 at 30 fps needs 3500 and more bandwidth. At 60 fps 4000 and more - not feasible with Twitch non-partnered.
So the choice is easy:
- in OBS, use output mode "simple".
- for streaming, choose nvenc as encoder. video bitrate 2500 or 3000 (test your internet connection)
- for recording, choose nvenc as encoder and use "high quality, medium file size" or "indistinguishable quality, large file size" quality setting
- in the "Video" tab, set base (canvas) resolution to your native screen resolution
- in the "Video" tab, set output (scaled) resolution to 1280x720
- in the "Video" tab, set fps to 30
This way you stream and record with 1280x720.
If you want to stream at 1280x720 but record at native screen resolution at the same time, use this:
- in OBS, select the "Output" tab and set output mode "advanced".
- in the streaming sub tab, choose nvenc as encoder and...
- check "Enforce streaming service encoder settings"
- check and set Rescale output 1280x720, Rate Control CBR, video bitrate 2500 or 3000 (test your internet connection)
- the other settings leave as default
- in the recording sub tab, choose nvenc as encoder
- uncheck Rescale Output, set Rate Control CQP, CQP value 20, preset high quality, profile high, other settings leave the defaults
- select the "Video" tab
- set base (canvas) resolution to your native screen resolution
- set output (scaled) resolution to your native screen resolution as well
- set fps to 30
It's a bit more complicated to set up, but this way you can stream at one resolution and record at a different resolution. If NVENC doesn't work for both, try to choose Quicksync as recording encoder and still use CQP (or ICQ, if available). NVENC is better for streaming than Quicksync.