Paintball Ballistician :P
Just to add, if you are really set on a particular rating (i.e. Machinery Repairman), and you're qualified (determined via ASVAB), the recruiter may tell you there are no openings and he may not be lying to you. It may be that there are no openings for the school at that time. In which case, he may tell you such or, he may try to get you to join and then 'strike' for that rating once you're in.
Striking is a process in which you are essentially a generic, very junior sailor (E-1 to E-3), and you are going through the processes to become "Rated" (Machinery Repairman aka MR is a "Rating"), while at your first command. This process usually entails, at the minimum passing a multiple choice knowledge test; at the maximum, attendance of a formal navy "A" School (a course several weeks to several months long). Often, it's completing various job qualifications, getting the approval of your Commanding Officer, and taking the test. I can't tell you if MR requries an "A" School but, I suspect it does.
Ratings that require a school can be a little tougher to get into. That's because (I'm oversimplifying a bit) your command essentially pays for you (your barracks, your food, your wages) and they need to pay for you whenever you temporarily leave the command (i.e. to attend training). The net result being is that you often don't get to go to the school until it's time for you to transfer from that command, while en route to your next command. This is because your originating command doesn't have to pay for you but, rather the Detailer does. The "Detailer" in this case is the individual responsible for the assignments of all the MRs in the Navy (and all rates in the Navy have their own Detailers).
Entering service with a plan on "Striking" is a gamble. If your first assignment is one of those locations that have a machinist shop, then that's a good start. If you end up elsewhere (i.e. smaller ships or aircraft squadrons) that may not work out very well at all.
Another option the recruiter may offer is for you to get into one rating school, only to subsequently transfer to another rating. The process is similar to "Striking" and has the same hangups but, adds consideration of how well your current rate is manned vs how well your desired rate is manned. For example, if you get in as a "Machinist Mate (MM)" who specializes in large machinery [engines, etc] operations, and ask to transfer to MR, it may be that the MM community is undermanned, while the MR community is overmanned and therefore, you cannot transfer to that rating.
And it is entirely possible for one to get an "A" School assignment as part of your enlistment- it will be prominently called out in your contract so, don't sign unless what you want is in the contract. However, just because you got the "A" School assignment, if you flunk out of the school, you're at the mercy of the Navy's needs.
If you enter the Navy without any such guaranty, you are entering as "undesignated". While in bootcamp, you will have the opportunity to decide between a handful of undesignated communities and attending their respective 'apprenticeship' school. These include: Seamen, Airmen, Firemen, and Constructionmen. Generally speaking, Seamen learn how to handle boats and ships (tying them to the pier, sanding, painting, etc), Airmen learn to handle aircraft (guiding them around the runway, maintaining/operating the landing gear on the ship, cleaning the aircraft), constructionmen learn to become SeaBees (construction of buildings and other structures), and firemen learn to do basic Hull maintenance, damage control for the ship, etc. undesignated 'apprentice's (i.e. Seamen), are expected to start the Striking process when they get to their first command.