Depends on how long you've been in when you get the promotion. Less than two years... about $250.
Get used to using the tables on this site... http://www.dfas.mil/
But if you're going in without a degree... depending on your rating... it might take a year or more before you're considered eligible to take the test for advancement -- as I recall, the advancement tests are given about every six months. Then it's based on how you do on the advancement test whether or not you make rate ("sew on your crow" or advance to Petty Officer Third Class)... and you're competing with every other E-3 in the Navy who's after the same advancement.
Based on your test scores... all of them... and the composite scores... you'll be given a laundry list of ratings from which to choose. If you took the ASVAB without preparation then the list will be indicative of the jobs for which you're best qualified. Feel to pick any one of them that suits your fancy. If, on the other hand, you crammed, and practiced, and otherwise prepared... the test results only show how well you can learn to take a standardized test... and the laundry list will be rendered virtually meaningless.
Do your research on the jobs now. Go to the ASVAB home page and wander through the links. There used to be one for Navy jobs. But you may not know all the composite scores (scores arrived at by adding scores from selected parts of the test together... or using some other formula). The "78" is a percentile score. What that means is that you're at the top of the lower 74?f all those who have taken the test. Do Google searches on those jobs that sound interesting. Talk with your recruiter. If it's your intent, tell your recruiter that you want to make the Navy a career and would really appreciate some advice. Do NOT ask, "Which is best"? That's your decision. But it's certainly appropriate to ask what it like to be a (whatever the rating)... what they do... what the "A" school is like.
Since you're considering on being career Navy... presuming that's your intent... you don't care which ratings relate most closely to a particular civilian job. The answer to that question is that the Navy trains you for a NAVY job... what a recruiter tells you notwithstanding. They train you on Navy equipment. They teach you Navy systems and procedures. You practice with Navy applications and scenarios. Any of that training that's applicable to a civilian job should be considered a bonus.
The ratings that are in demand today really aren't going to make much difference if you're going DEP. By the time you go in, it'll probably have changed. Do your research, find those ratings that appeal to you. If you get offered one of those, go for it. If not... well, you might be surprised to find one of those jobs you thought you wouldn't like... it might be really enjoyable.
I enlisted in the Navy at age 20 with a BA in Math. Thought I might get into the (then) relatively new field of computers. The Navy had other ideas and my rating picked me. It had nothing to do with computers and very little to do with math. The degree gave me about a year lead on those without the degree and I made rate rather quickly. When it came time for me to reenlist for my E-6, somebody discovered the degree and recommended me for OCS (Officer Candidate School). I took the offer and retired at age 45.
My Navy experience was pretty awesome. I went places some people might not have even heard of. I got to do stuff a lot of guys can only dream about doing. Spent a couple of tours in DC... the "belly of the beast"... the Pentagon. Hope yours is as enjoyable.