That description requires P-channel MOSFETs. Fewer choices, pricier.
Are you sure you can't connect battery + to motor "+", motor "-" to MOSFET drain, MOSFET source to battery -/Gnd, and drive transistor gate from arduino?
You keep saying resistance - resistance, Rds, is property of MOSFETs.
If you want low resistance, and thus low voltage loss as V = IR, then you want a MOSFET.
BJT transistors have a voltage from collector that is pretty steady, independent of current. If you want to give up 0.7V of your 3V (4.5V? 6V?) in the transistor, and thus have a slower motor, go with a BJT transistor. PNP per your description, NPN per mine. Look for a low Vce at saturation, then search for the Ic current the motor needs.http://www.digikey.com/product-search/en/discrete-semiconductor-products/transistors-bjt-single/1376376?k=pnp%20transistor&stock=1