What's the problem with overkill? Overkill's a good thing, unless you're trying to shave every last tenth of a cent off the manufacturing cost of a high-volume consumer product. Otherwise, overkill is called design margin or safety margin-- the quality of being much more than minimally sufficient for the job at hand.What I need to know (or why I need to know) the current so I can select a MOSFET that will suit the purpose without any overkill.
And "minimally sufficient" is what the 2N7000 you mentioned is: it's a small-signal MOSFET rated at only 200 mA, barely more than the motor current you mentioned.
A better choice for driving your motor would be one of the "logic-level" MOSFETs. One good one is the IRLZ34, which has a low gate-to-source threshold voltage and an Rds(on) of only 0.05Ω when driven by 5V Vgs, so you'll lose almost no voltage at your motor. Price at Digi-Key is about $1.03 US-- not quite as cheap as a 2N7000, but still cheap.
I keep a parts drawer full of them; they're handy for all sorts of things.