Lithium primaries are the best for long term storage, but D cells are only available in 3.6V configurations, so you will need to build an adaptor to avoid frying your lights.
Low Self Discharge NiMH rechargables are second best, and are available in C and D sizes, but you take a considerable loss of capacity with all be the most expensive batteries. These are best for daily use lights. As an example, I rotate 2 sets of AA batteries through my kid's night light (1 set in a cheap charger, 1 set in the night light).
You can use alkalines, but there cannot be any metal to metal contact, like an aluminum battery tube, if you want to avoid corrosion. I lost one 2D maglite to battery corrosion and I've had to repair my wife's MiniMaglite twice for the same problem. However, our ancient, plastic bodied Rayovac and Brinkmann 2D lights had near zero corrosion despite holding the same batteries for several years.
IMHO, If you want to continue using alkalines, consider plastic "C to D", "AA to C", or "AA to D" cell adaptors so there's no metal to metal contact. I believe you can get 2AA and 3AA to 1D adaptors, but I can't vouch for their quality.