How to choose an electric engine for a motorcycle?

First of all, there is no such thing as an electric "engine". It's electric motor.

That being said, what you might choose is entirely up to what you are trying to accomplish. Engines for vehicles are usually rated in HP while electric motors are usually rated in Watts or Kilowatts. But one system is easily converted to the other using the formula:

1 HP = 745 Watts

Let's say we have a typical 750cc motorcycle engine that makes 50 HP. I know, some make more and some make less, but let's assume you want 50 HP.

So that is going to take an electric motor rated at 50 * 745 = 37 KW

That's an odd number and most motors come in increments of 5W so we might round down to 35 KW. Now you search for some DC electric motors that are in the 35 KW range. Pick one you like.

Now you need a motor controller. Search for DC motor controllers that can handle at least 35 KW (or design your own) and get going on that.

Finally you need a battery. How big depends on how much range you want. Keep in mind that you don't need to supply 35 KW 100% of the time. What does your riding profile look like? Let's say you are going to want an average power of 5 KW. If you want 100 miles of riding at an average 30 miles/hour that's going to take:

3.33 hours * 5KW = 16.6 KWh of battery capacity.

Ok, so now you buy or build a battery pack that fits into the space you have left on the bike.

Some other things you might consider:

1. Regenerative braking
2. Charging controller