How much motor do I need for my electric-assist bike?
A highly trained competitive cyclist can ride at ~ 350-400 watts of power output for a 2 hour ride.  So adding a 400 watt electric assist motor is roughly equivalent to adding a competitive cyclist 'stoker' to your rig.  The speed and battery size make a big difference but here are some rules of thumb:


Some motors are measured in horsepower, rather than watts.  1/2 horsepower is roughly equal to 400 watts for this use.
A 400-watt motor will usually be sufficient for the average rider. Your rig is a little heavier, so you might want to go with higher watts.
On a typical 400 watt rig, two 12-volt, 12 amp-hour batteries will take an average rider 10 miles at 15 mph or up a hill that's 800 feet tall.
To go faster (assuming you haven't maxed out the watts) or further, you need to increase the battery - range is proportional, so twice the battery size = twice the range at the same speed.


There are companies like Convergence Tech that sell kits for motors in the 1 horsepower range that are pretty easy to add to an existing bike if you are mechanically inclined.  That range is probably more than sufficient for your needs.

Be aware that some areas limit the top speed or the available power for electric or gas-assisted bicycles.  I've seen speed limits of 25-30 mph and power limits as low as 500 watts.  You will want to check with your local road or transportation department to make sure you comply with local regulations.