It's probably easier to get a $99 kit like this one, if you don't have good metal working facilities. I think you might want to replicate this arrangement, which uses a free wheel that screws into a single speed sprocket. If you can get that part, then add a chain and some metal brackets. Motor gear might work. Zoom zoom?
For $180, I can get a nice 500W geared motor with wheel and electronics off ebay. I run mine on a $280 36V 10AH battery from China, but have also run it on my Ryobi Weedwhacker battery, which is 36V and about 2 AH. In fact, I ran it for 11 miles yesterday at 14 mph on pedal assist before I used up all the power. For throttle only, I'd be lucky to get 4 miles at that speed.