If you are really good at math and score well on your ASVAB, I'd go Navy. The Nuke program will pay you gold, you get hazardous duty pay virtually right off the bat, you are immediately an E3, and when you finish school you will be an E5.. meaning tenure. You are now an E5 without even leaving school, and school you get pampered along with the studying (there's alot of that). Plus, you can have a Bachelors in Nuclear Physics within 6mo of school completion. Also, you get to choose Sub or Carrier. Carriers are awesome because you're in the belly of the CV, and the rest of the 30 or so tenders sole duty in life is to protect your CV. So here you are, on the ocean, with massive bulk to begin with, shielded by a multitude of others and aircraft while making your own personal hot water and having a good time about it. (it has some hard spots, but it's awesome). If you do really well, they will also offer you Officer School.
Navy sees more of the world as well. Ports are awesome for the leave etc etc. If you want a sub, go boomer, you'll most likely never see combat but have to sleep between the worlds second largest nuclear arsenal. You can plan a life, it's always a 3 on 3 off deployment. Meaning you can plan you children's births so you are home!
Oh, the signing bonuses... I'm not sure what they are giving now for Nuke's, but when I was in, it was about $100k for signing. (most was schooling, rest was cash). I know they still pay well though, Nukes are hard to get through school. It's like a 6-8yr college education in less than 18 months so they need to get people signed up to compensate for a 75% drop out rate (that's before the fail outs). Bad side is if you don't make it, you are immediately a submariner.
Good luck on your choice, I have friends and family in every Branch. They all suit different types. If you do choose Navy, don't do boot in the summer or winter. Great Mistakes is hell during those seasons.
Marines get the most women of all the branches.