The Navy is always looking for Nukes. The amount that leave after their first enlistment demands that.
Since the Navy also chooses your rating I wouldn't get too hung up on wanting MM. Even though it is the easiest rating of the three to get.
In regards to shore duty for nukes...once you finish all three schools you'll basically be on a sea command for the duration of your first enlistment. At least that's what I'm being told is the "norm" for nukes.
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