I'd suggest an electric rear hub motor. The motor is in the hub of the wheel. There are different voltages from 24 volts to 52 volts and various sizes of batteries. Size of battery is usually expressed in amp hours. This is the amount of charge the battery will hold and governs the distance you can travel.
I'm 78 and electric bikes are the most convenient for older people. I'm sure the other electric bike builders here will fill in information.
If you decide you want gas instead of electric then do a rear rack mount either chain drive of friction drive. You'd have to get rid of the rear basket. Staton Inc has some really good rear mount kits and friction drives.