At 5'7" a 24" bike is small for you. Look in your area on craigslist. I did and this is the first thing I saw:
Schwinn Varsity Road Bike
A 24" bike limits your tire selection, as you have already found, and since they are made for a smaller person, it's not made very strong, and probably wouldn't be adequate for a motor conversion. A bike that fits you well is a lot more important than most people realize, but if it doesn't fit you well, you won't ride it, and it won't help you. Would you like to walk those 3 miles in shoes that don't fit? Get a bike that fits with a comfortable saddle, before you start thinking about aero and motor conversion.
If you get a 26" or 27" bike you have a lot more tires to choose from. Even with a knobby tire, if you pump it up to about 50 lbs, you are reducing the RR a lot. Be careful though, because it's easy to over inflate and pop it off the rim. That will blow the tube and you'll have to buy a new one.
Aero doesn't make any difference on a bike until you get above 15 mph, and if you have a hard time with 3 miles, you're a long way from being able to maintain that speed long enough for it to make any noticeable difference.