As a USNA grad I'd say you made the right choice. Go Navy!!
You are correct the at USNA nearly 100% of midshipmen who choose Navy Air get it. As for your chances of flying TacAir (Navy for tactical jet aircraft), that's pretty good too. Not many "heavies" in the Navy, but there are some. But there are also lots of helo pilots in the Navy. Lots.
What you end up flying depends mostly on your flight school grades. If you get good grades, you get your first choice. It's that simple.
And you are correct that USNA has produced more astronauts than any other school, including USAFA and USMA combined.
Life aboard a modern nuclear carrier is not bad. Especially now that women are allowed on carriers. Much nicer than in the old days. And you get to see some great places when deployed.
Navy pilots rotate from sea duty to shore duty every three years or so. You only go aboard a carrier during your sea tour. Yoy typically go on two or three 6-month carrier deployments during your 3 year sea tour. The rest of the time on a sea tour you're at a land base, doing training or "working up" for a carrier deployment.
Shore tours can be flying related, or not. If you're making a career of it, you need to get a masters degree, attend war college, serve a tour in the Pentagon or Crystal City, and other stuff during your shore tour which will prevent you from doing much flying. Or you can go to Test Pilot School (TPS) or fly for the Blue Angels, or become a base pilot. There are lots of flying related shore tours, but they may be limiting if you want to make Admiral. To make Admiral, you gotta punch the right "tickets", which involves politics, which means time in the puzzle palace (Pentagon).
Hope this helped.