It really helps to store your sails in a "sausage" bag. This long bag allows you to store the sail lengthwise, flaked down in the tube. The bag has a velcro or zipper along the full length with openings on each end that allow you to attach the sheets, tack and halyard while the sail is till in the bag. There are also straps to secure the bag to the stanchions if desired.
So.. what you do is flake the sail in the bag, zip up, THEN fold it in thirds so it can be stored below. IOW the sail and bag are folded together, not the sail folded inside the bag. You can unfold the bag as you bring it up on deck through hatch.
Whether you use the sausage bag or not it is importent to flake the sail so the luff stacks on top of itself, rather than the traditional pyramid form most of us do on the dock. This makes feeding the sail in the groove a whole lot easier come hoisting time.
When you take down the sail you can flake it right into the bag on deck. Zip it up, and it's ready to use again.
Regarding sheets, you'll need an extra set if you're not going to tack when you peel. Otherwise, you can take the lazy sheet from the old sail, hook it to the new sail so when you tack the new sail has the weather sheet, the old sail is now inside (weather). Peel the old sail and attach the lazy sheet to the new sail... fold the old sail into it's sausage bag and get it below... you're good to go.