This might help identify:http://tncscooters.com/index.php?route= ... path=41_73
Most of them have a document linked for a wiring diagram.
I recommend the LBD14. Yes, they are usually limited to about 30 amps. My turnigy wattmeter has validated this a number of times.
Look inside any controller and you'll see some FETs and some capacitors. The FETS tend to be about 60v rated, and the caps about 50V. So if you don't go over 50v on these cheap and cheerful units you're ok as you won't "let the magic smoke out" of the components. All that matters then is your low voltage cutout, and your max power = your voltage times ~ 30 amps.
Yesterday I got a nice city tyre (smooth on top, knobs on sidewalls) and pumped it right up on the rear. Picked up about 7kph cruising speed, top speed too. Tyres matter.
To connect your single phase controller, all that usually matters is the four fat ones (Power in from battery and power out to motor) as well as the key switch. Unless the keyswitch leads are connected together, you'll get NADA. Which is how a keyswitch ought to work...
I usually take all the other plugs such as brake lights, charging port etc and tape them up in a big bunch out of the way.
Single phase brushed controllers are nice and easy, not as daunting as getting a 3 phase brushless one without labels. Hang in there.
AND USE A FUSE
Keep us posted!