O.P. is in the U.K. and I doubt that he has a Harbor Freight nearby or access to a Briggs and Stratton.
The engine that you link to states the engine produces 1.1 hp. This isn't going to be enough to power to take off from a standing stop or go up any hills, unless you weighed about 90 lbs. You would have to pedal to help the engine along. Another issue would be finding a clutch to fit that engine or how to make it into a friction drive, not knowing what the engine shaft looks like.
What type and size of engine depends upon how you want to mount it, your weight, 2 stroke or 4 stroke and what is your purpose - do you want the engine for pedal assist or do you want the engine to fully power the motorized bike. Many people have built friction kits with 4 stroke 35cc Honda and Robin engines. However, these engines are more powerful due to their modern designs.
You can convert a vertical engine to run horizontal. You can also use them as friction drive, but these are bigger engines than the one you referenced.
Here's a YouTube link how to convert a vertical to horizontal and a MySpace page of a forum member who converted a vertical engine to friction drive. i don't know if the information will help in your engine selection: