I was going to raise the possibility of an ebike in fun, but since the idea might be being taken semi-seriously,
@potsy's budget would get him something decent.
The Cube in the link has the Bosch crank drive motor, which is very like ordinary cycling, only easier.
No throttle, so if you don't pedal, you don't go.
It has speed, cadence and torque sensors, so responds to the effort you put in.
The bike is ridden just like an ordinary bike, you change down and pedal a bit harder for hills and head winds.
Fully road legal, so the assist cuts out at about 15.5mph - there's couple of mph tolerance in the regulations.
Above that, you are on your own.
The crank system has no resistance, so all you have to propel is the extra weight.
Cruising in favourable conditions above 15mph is doable, and when you drop below, the motor cuts back in seamlessly so it's possible to make smooth and swiftish progress.
The Cube has the bigger 500wh battery, range is very much a piece of string question depending on conditions and which assistance level you demand from the motor.
Tour setting - level two of four - is a reasonable compromise between range and assistance and should give between 40 and 50 miles.
http://www.cube.eu/en/products/e-bi...oss-hybrid-race-allroad-500-blackngreen-2016/