I'll put in my two cents as a former Penn State mid. Some of this has been hashed out already, but GO ROTC, at least for a year. I was in similar shoes to yours at the end of high school. My Grandfather was USNA class of 1941, a mustang sub officer back in WWII. I was rejected from the Naval Academy (my first choice) and bummed out about having to go to a civilian college for a year before I could reapply. Every ROTC unit can send 2 mids a year to Annapolis, and my freshman advisor told me straight up that if I still wanted to go there, he'd help me if I busted my ass. I ended up staying ROTC, but the opportunity was there. I decided it wasn't for me.
Here's my rationale looking back. Your college years are a unique part of your life, no matter what school. Trust me, you'll miss them when they're gone (damn that sounded like an old fart). There's much non-military-related to experience at a civilian college, ESPECIALLY a big school like PSU, that will enrich your time. This includes a wider variety of people to interact with, a wider variety of classes to take, and a wider variety of ways to screw up. You'll learn a little of how to relate to the civilian world and yes, deal with those a$$holes who think we're all a bunch of baby-killers. You're in uniform amongst the civilian population, not locked away in Bancroft Hall. Side benefit to THAT is it's also a whole lot easier to blow off steam, whatever it is you do to do that.
The military aspect is still there, just not 24/7, which in its own way is good. In your military career you'll be out in the real world anyway, and won't wear the uniform 24/7. Don't think that you won't get a quality education in what it takes to be a military officer. You will. Penn State NROTC staff was for the most part top notch during my time there.
However, much of ROTC is what you make of it. You can do the minimum and coast by, or you can grab it by the balls and get a lot out of it. If you want challenge at Penn State, take a technical major, join Basic Drill and PT with the Marines and the SPECWAR folks. That's plenty on your plate for one year. It's also the way to get noticed if you're looking to reapply to Annapolis. And those As and Bs come a lot harder in college than in high school, especially in Physics and Calc, trust me. I've been out of the loop for a couple years, but PM me if you want any Penn State related gouge, I can give you the names of some others on the board to talk to.
Bottom line, I'd take the scholarship. Go to PSU, go through the Gap and then decide if you want 7 more weeks of that crap (which would be Plebe Summer at the Academy). Go live in East Halls with 1700 other crazy 18-year-olds. Then go to a PSU football game and decide if you'd rather spend fall Fridays in your SDBs, or with 106,000 of your closest friends and a party waiting afterwards. Then spend the rest of the year in NROTC at a real college. If you still want the Academy at the end of that, the only one keeping you from it is you. The word you got on statistics is news to me; I was under the impression that NROTC had an in with Annapolis. That said, work hard and the unit will put you there. The heck with 22%; your chances of making it to Annapolis are either 100% or nothing, and it's all on you. If you decide to change your mind, then your commission comes a year early and it's written on the same paper as the guys from Canoe U.