Either way you go I would highly recommend doing college one way or the other. Whether you go there first and join as an officer or whether you do your four years and get the GI bill and go to college for FREE with some spending cash.
If your parents are willing to help with college all the better, that'll be just that more spending cash you have while you attend college. With that and the new, post-911 GI bill you could go to college more or less for free and live comfortably while you do it. Absolute win-win.
As for Army or Marines I guess it all depends on what you want to do. I was a USMC infantryman for 5 years plus reserve time. I've spent about 6 years working as a government contractor after that both in the States and overseas. For the past 5 years I've worked with guys from all branches of service and with current and former members of the special operations community.
Basically, if you just want to do your 4 years (maybe a little more) and be done I say go with the Marines. If your looking to make more of a career out of it and move into specialized programs then I'd say Army.
The Marines will flat out give you the most experience that you can get as regular infantry in a four year enlistment. You'll travel the world, not just Iraq and Afghanistan but the Mediterranean, Asia, South America, all over. You'll train for ALL environments and you'll do it regularly. You'll basically do everything you can possibly do except jump out of an aircraft. If you're sqaured away physically and mentally you can try out for Recon or Marsoc and at some point they will send you to jump school.
As for the Army, it's a little easier to get into and life will be a little bit easier through your enlistment. Over time though, the Army seems to have some career perks over the Marines. Much faster promotion, a lot of schools and formal training, higher retention bonuses, and nice career paths for senior enlisted (lots of warrant officer programs).
You can jump out of planes but you have to remember: these are all low altitude static line jumps. As regular infantryman you won't be doing free fall jumps which I know is what you're thinking. 1000ft on a C130, stand up, face the back, and march out the back of the aircraft. The static line pulls the cord for you pretty much as soon as you exit. It's still pretty cool but probably not what you're thinking it is.
In order to do the cool stuff you probably have in your head you're going to need to get into the special operations community. That is another benefit the Army has over the Marines: a huge special operations community. There are simply a lot more ways to get under the umbrella of SOCOM through the Army than the Marines.
However you can't just join the Army and expect to get right into the special operations community. You can enlist with a special forces selection option but it's highly selective and a decent chance you'll wash out. So you can try for it but there's no guarantee and it will be harder than anything you can possibly imagine.
So again, for the short term bang for the buck you will do a lot more in the Marines in the span of four years than the Army. But if you're looking to make a career out of it the Army just has better perks for the long term.
As for future career, nothing against Police but I'd recommend setting your sights a little higher. Get into some kind of Federal LE, whether it be DEA, FBI, USSS, DSS, Marshalls, etc. In the end you will get treated better and make a LOT more money, like ~100k or more with shift differential and overtime and benefits. But you will need both military and college to really be competitive for hiring.