There are many different spackling products out there. I use the Dap vinyl spackling paste for most cracks and holes in drywall and just about every other material. It doesn't shrink, it's strong, it's somewhat flexible, and it sands easily. You just need to stir it a little more than the dryer spackles, since it tends to separate when it's sitting on the store shelf.
As for the ceiling tiles, I would try to clean them first with some kind of degreaser (diluted) and see if that works. If they are stained really bad, you may need to use a stain blocker, like kilz. Stainblockers now come in spray cans that spray upward.