About everything I use these days runs on AA's or AAA's, the division between those two types being pretty even. So those are my standards. I buy them in the largest packs I can find when they go on sale. My personal experience is that RayOVac alkalines perform as well as, and leak less frequently than, Energizers or Duracells. Plus, they're cheaper and come in even bigger bulk packs. YMMV.

Smoke detectors take 9v, and I buy those only as needed at daylight->standard time changes, when I change all my detectors. I have some old MagLights that run on D's and C's, but I never use those much anymore and don't keep spare batteries on hand for them. If I need D's or C's, I only pick them up at the store at the time of need.