I have a 2 hp 2-stroke Suzuki on my Harpoon 4.6 (15').
I would suggest small and light for a 13' boat. If price were no object, I'd consider a Torqeedo with a spare battery pack for increased range. Next down from that might be a Lehr 2.5hp propane powered outboard, because it just seems more simple than a gasoline engine, what with stinky gas, and mixing oil for a 2 stroke. There are quite a few Honda 2 hp motors on my lake. They are air cooled, which makes for less maintenance in that you never have to replace a water pump impeller, but they tend to be noisy. Given that, replacing the water pump impeller on my Suzuki involves removing the prop, undoing 2 bolts, and swapping impeller. Quite simple. You may also consider a 55-65 pound thrust transom mounted electric trolling motor. The drawback to a trolling motor is finding a place to store a heavy deep cycle battery. I do know some people who only ever motor short distances who use a "jump start" battery with the trolling motor. Come to think of it, that one guy uses a small gas motor and the trolling motor on a wider mount pad. Most of the time, he motors in and out of the marina with the trolling motor and the jump pack, but if he were becalmed on the other side of the lake, he would still have his gas motor for extended use. Best of both worlds... I have heard of much longer run times on a Torqeedo motor than I would have expected, so perhaps the Torqeedo is the best of both worlds, especially with that second battery.
The thing I HATE about my Suzuki is that I MUST shut off the internal fuel tank valve, and run the gas out of the carb bowl. If I do not do this, and I tilt the motor, the fuel in the bowl runs out into the engine cowling and stinks to high heaven. As an added precaution, even when I do run the fuel out, when I tilt the motor, I rotate it such that the face of the motor (and air intake of the carb) is pointed upwards, to eliminate any chance of fuel leak.
For new motors, the best blend of motor cost per range is going to be a gasoline motor, with a Tohatsu 2.5 4-stroke around $870. A Honda 2.3 is just under $1000. Yamaha 2.5 is probably just over $1000. Next would be a Lehr due to prices around $1050, and then the Torqeedo Travel 503/1003 priced about $2000. All prices I've listed are quick internet surveys of new motors.
Of course, if you can find one used for $400 or so, you may be in good shape.
If you get any gasoline engine, check out
www.pure-gas.org to see if you can buy ethanol free gas nearby. You can also consider Sea Foam additive.
Hope this helps,
Brian