Square 9V batteries are only good for a couple hundred mAH. That's why the Lego NXT whatever they are called used 4 or 6 AA batteries - 2500mAH capacity.
I use digikey.com to find MOSFETs, filtering as I go:
N-channel MOSFET
FETS-Single
IN-stock
Logic level
Through hole
Sort by price, low to high.
Then scrol down the list, find the lowest Rds and Input Gate capacitance you're willing to pay for:
http://www.digikey.com/product-search/en?FV=fff40015%2Cfff8007d%2C1140050%2Cefc0005&k=n-channel+mosfet&mnonly=0&newproducts=0&ColumnSort=1000011&page=1&stock=1&pbfree=0&rohs=0&quantity=&ptm=0&fid=0&pageSize=25
AO1516 and AO1518 both look pretty good.
Wire the motor up for low side switching, connecting '-' lead to Gnd thru the MOSFET.
Don't forget a 1N4001 type diode across the motor, anode to +9 and cathode to the MOSFET Drain, with Source connected to Gnd.
Arduino to 220 ohm resistor to MOSFET Gate.