One more comment, here's a few pieces of advice. Please keep in mind that this is coming from someone who has never served, and is commenting as someone who works with former military members in a law enforcement agency, so I'm like a bystander looking in.
I would strongly suggest that you apply to a law enforcement agency of your choosing while in the military, because it takes (depending on the agency) approximately two years to get through the process of testing, the physical fitness exam, the interviews, backgrounds investigation, polygraph, and psychological evaluation prior to the academy. I know guys who applied towards the end of their contract so they can hit the ground running as soon as they got out. But they weren't able to do any of the testing and interviewing until they got out due to scheduling conflicts.
The academy, depending on the agency, can be anywhere between 5 months to 8 months. It all depends on where you go. The FTO period is another 3-5 months, again depending on where you go. And through this whole time, you can be dropped for anything. I've seen former military guys who were deployed and been in combat excel, and I've seen some who didn't make it. The same can be said for college graduates, and even guys who have neither college or military experience. It all depends on YOU.
If you want to get into SWAT: Our SWAT team consists of a mix of former military, and just regular cops who've worked the beat for a number of years. Of course, with military experience comes training that a lot of the beat cops haven't received. But keep in mind that they will teach you how to do things THEIR way, which isn't necessarily the Marine Corps way. If you're looking to get into SWAT, just keep your nose clean, don't get too many complaints, don't get sued, and pass the interview process and physical requirements (my department has a PFT for SWAT that is pretty much in line with the Marine Corps PFT, except if you want to stand out you have to get max, which is basically equivalent to a 300 on the USMC PFT).
Overall, it seems like being prior military is definitely a plus, and if you have a degree on top of that, you're pretty much a perfect candidate to be a cop. Nowadays however, with the amount of bad press and attention police get, it seems departments want to shift to a more "community friendly" and "gentle" approach to law enforcement. The days of the cowboy, vigilante, hard charging, kick ass and take names, Dirty Harry type law enforcement are long gone. It's not like that anymore and hasn't been for a while.