When I went in (1982), the enlistment bonus was only $2000.00, paid upon completion of prototype. Reinlisting for 2 years was another $20,000.00 (very tempting in 1984). I had an associate degree, and no job to make payments on my loans. Looking back on my situation today, I would have done the same thing again now. I knew what I wanted when I went in, and stuck with that. I went in for the training and got out after the minimum of 6 years (I understand that it is now 8 years???). Sometimes I wonder what it would have been like had I put in the 20 years. I would be getting a monthly check and living a lot easier now financially, but my family would have suffered. That is water under the bridge for me, but something for you to consider while you have the opportunity.
The comment about EM rate and working their #$% off in carbon dust is correct. In my opinion, the choice of rate would be the ET, followed by the MM, only if you can also get ELT, and then EM. If you put MM anywhere other than 3rd choice, you will most likely be an MM. I put ET, MM, EM, and my associate degree is in electrical power. I became a MM. I have poor study habits, but good retention once I see or hear something. My grades were good enough to get the ELT school without adding 2 years, so good grades can pay off. ELT school has done more for me than any of the other nuke power school stuff in the outside world. Being a petty officer in the nuke navy is standard (I saw only 1 who wasn't in my 6 years, and that was a reduction in rank issue). But if you happen to wash out of the nuke program for some reason, you will be ahead of the others in the conventional fleet.
Navy life for a family person is not easy. I have seen many marriages broken up due to the frequent and long deployments. If you want to see the world, when you get to the fleet, a carrier or a fast attack boat are the best choice, but if you have a family, a boomer is typically better with a 90- 120 day out/in cycle.
Good luck in you carreer.