For painting these walls, should I just paint over it the new color?
Stripping or sanding existing paint off of a wall isn't done unless the paint is really bubbling or chipping off.

For painting walls, the best way to go is to clean the walls, put on a coat of primer, and then finish with 1-2 coats of a latex paint.

Primer will cover an oil or latex paint and give the new paint a uniform layer to adhere to.  This is good because you say that the wall might need patching.  The patched area and the original walls will take paint differently and could end up with a different sheen if you do not prime first.

Now, this could be somewhat region specific, but I don't think so.  Interior walls are normally painted with a latex based paint.  High traffic areas will use a glossier paint to make it easier to clean (bathrooms, kitchens), and bedrooms normally use a flat, non-gloss finish.  Oil-based paint is still used in limited application for trim, but really most of that is also latex.