Things I do to speed things up in Windows Vista/7 (might work for Win8 but your slowish PC is probably not running it
):
1) Open up Services (Windows key + R, and type in 'services.msc') then Stop and Disable the Windows Update and Windows Search services.
2) Go to Remote settings in System Properties (Windows key + Pause/Break) and make sure Allow Remote Assistance is unchecked.
3) Disable anti-virus software when streaming.
4) In OBS make sure it's using the 'ultrafast' setting under Video in Advanced. Also, and I'm not sure if this is related to optimal stream speed or just quality, but apparently Twitch prefers 160kbps/stereo. I think a higher bps setting (like 320) will be easier on the CPU but it will take up more bandwidth.
5) Disable any unnecessary startup programs. (run 'msconfig', click Startup, and go down the list of programs - but be careful what you choose to disable!)
Most of these apply if you're running XP. Note the list is not complete; I'm sure there are other tricks.
It's probably worth Googling OBS for slower systems as there's a lot of settings related to the video encoding (keyframe etc) that might be useful to change.
BTW, generally it's not recommended to disable Windows Updates as in 1). So be sure occasionally to temporarily re-enable the Windows Update service and manually check for any new updates!
EDIT: For 2) disable Remote Desktop also.