A lot of what you can or cannot do in the Navy depends on your ASVAB score.
Most rates have a base ASVAB score to join. The higher the score the more options that are available to you. The highest you can score is a 99, the minimum you can score and join with is a 35 (31 for reserves)
What you might not know is that your base score in certain areas of the test add up to overall scores that meet the threshold for that rate. So your overall score might be lower than average but you did well enough in certain areas to get into the rate.
Here is a chart I found online
http://usmilitary.about.com/od/navy/l/blasvabscores.htm As far as ratings (basic enlisted job groups in the Navy) there are many,
Here is a list I found online
http://usmilitary.about.com/od/enlistedjob1/a/navyjobs.htm Within these rates there are NECs (Navy Enlisted Classifications). These are specialties within your rating you are trained for. An example might be you are an AT (O level) (Aviation Electronics Tech) with the NEC AT-6615, you would be a FLIR camera tech on P-3 Orions. As your career progresses you can keep getting more and more NECs as well at OJT on more systems.
Here is a list of NECs I found online
http://usmilitary.about.com/od/navynecs/a/necmenu.htm It might seem like a confusing system at first but once you are around it awhile you get use to it.
Now there are other options as well. If your base ASVAB is not high enough you can “strike” a rate by joining as an undesignated E-1 then when you are eligible you can take the third class test for the rate you want without going to the “a” school for that rating. This requires a certain level of dedication.
I would start your search by looking at ratings. General job groups. I am an ET (Former AT who cross rated over) I am very happy working on electronics. You might be more into admin work, ratings like AZ, PN, or YN might be more appealing. Computers, be an IT. Like bombs, AO. Want to be an air traffic controller, try AC. Logistics? Try LS. Painting? BM. (Just kidding all your BMs, I know you guys do a lot of other stuff), welding? HT. The options in the Navy are nearly endless.
The officer community is another ball of wax and I think this is long enough to get you started…
Just remember that if you do not qualify for the rating you want you can take the ASVAB again after some studying or strike the rate after you have joined.
These are just the jobs.... you can do a lot of other stuff in the Navy... School... travel.... save money... a lot of other benefits...