Parking is free if you are staying at a Disney resort with or without an Annual Passport. Doesn't matter what, if any, ticket media you have. If you are staying off site, though, the only way to get free parking is with an Annual Passport.
I always call Disney World directly and order the Annual Pass vouchers. I get them usually in about 10 days. Once you get to Disney World, you have to exchange the vouchers at a theme park Guest Relations or Downtown Disney Guest Relations. You cannot do this at your resort. We usually do this at the International Gateway entrance to Epcot since they are never crowded and Epoct is almost always our first stop. MGM wasn't that crowded either.
Annual Pass discounts can be good. Not sure if you'll be able to get anything for Spring Break - they can block that time off since it's considered a premium time. You could get some breaks for the summer. But if you buy an AP, it's the perfect excuse to stop just thinking about going after the cruise and do it!