if you dont want to use flash then use the widest aperture ( smallest number)
The next thing to following here is that it will influence your depth of field. One issue with a wide aperture is low depth of field, so you might only see one person sharp when taking a picture of 2 persons.
You need to find your own system, I tend to use:
1) what is the light situation => what ISO do I set
2) what depth of field do I need => aperture setting
3) what shutter speed does this lead to => do I need a tripod (flash) or review lens, ISO and aperture, for the scene (VR, speed of subject, etc...)
exposure compensation is to trick the camera into taking what it believes is right but you know is wrong , ie snow shot the camera will want to underexpose to 18% grey so leave the settings and use exp comp by a stop or two in the plus and both you and the camera is happy
I use this in 2 cases:
1) in certain set-ups (macro lens with extension tubes) the camera systematically underexposes, to compensate this I use exposure compensation
2) some landscape scenes are wrongly exposed (not for the subject) due to a bright sky or a dark forest around it
The alternative is using the manual settings and allowing over or underexposure manually. You might want (for artistic reasons) to blow out the background, etc...