The rear wheel motor is the simplest and cheapest solution but a better one, imo, is the crank mounted motor. A TSDZ2 or Bafang would be the choice there. I have both rear wheel and crank mounted motors and the crank mounted is just nicer to use. The wheel and the Bafang crank motors use a sensor on the pedals that merely require the pedals to go round without effort for the motor to kick in whereas the TSDZ2 uses a torque sensor to kick the motor in so you actually have to pedal to get assistance. The motor kicking in when you are simply moving from coasting to pedalling is one I don't personally like. I prefer the motor to kick in only once my feet are firmly pedalling. It's purely my preference and not a fact that that system is better. I have two TSDZ2 units and got them both from here...
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A crank drive can use the torque multiplication effect of the gears whereas a wheel motor can not. If you opt for an ebay rear wheel then get one that has a display as the motor effort is controlled from the display (as are almost all motors). Get the displayless models and you get a non adjustable motor. I advise you to pay extra for waterproof connectors too. Basic ebay kits are not waterproof. You want julet or higo type connectors. If you get one with a throttle, apart from being non legal there is the possibility you rely on it and drain the battery much quicker. Whatever you go for keep under 1000W (only 250W is road legal). 1000W will propel you to 30mph and that's plenty fast enough for bike components. My TSDZ2s are 750W and will propel me at 25mph easily. If I upped the gearing they'd hit 30mph on the flat but I need the lower gearing for hills.
As to batteries you need to match the battery to the motor and your desired distance requirements. A 48V motor at 1000W will require a 20 amp draw so you need a battery with a BMS that will output a continuous 20A or better. If you get one that is less then the BMS will limit the motor to what the battery can supply to protect the battery from damage. A battery will have two amp ratings, one in AH which is a measure of the overall power it can put out until empty and one in amps which is the max output at any given time. AH will determine your distance and amps will determine what size motor it will drive fully.
Most motors come with brake levers that cut the motor out instantly. If you don't use them then many motors run on for a half second or so after stopping demand. I have never found this to be a problem and wouldn't worry about not having such levers.