A bc337 (max 800ma)would probably work well with a resistor to get you a base current of like 12ma you may be able to get away with a 480 ohm resistor, and if you want even less current consumption on the base a tip122 (max 5A) would work with a 1k resistor for <.005amp
and with 700ma on the tip122 I wouldn't worry about a heatsink, maybe a small one if anything, the bc337 I've never drivin to near max so idk about the heat on that