Q: Would I want to train my abs just minimally if I want a small waist? Doesn't it increase the thickness slightly if you have too much muscle there?

A: To some degree it's actually true -- your obliques (muscles along the front sides of your lower torso) can actually grow in size relatively easily and even make your love handles look bigger. It's not really the case with rectus abdominis -- the front of your lower torso. Rectus abdominis is a flat tape-like muscle that will only bulge out significantly when flexed.
Your abdominals will also be developed to some degree if you do big lower-body exercises like squats, deadlifts, and lunges (which you should!). Finally, you need to keep in mind that if you do not traing your abdominals you're making yourself vulnerable to lower back injuries and pain.

So after all this, my advice to you would be to continue training your abs, but only use light weights/high reps for obliques (or even drop specific oblique training altogether and rely on squats/lunges/deadlifts to keep them strong). You do not need to do a lot of ab training, but a few sets a week is a good idea.