As a 20 year old you would need to:
Do your CBT (£100-140 ish, days riding on a 125 basically),
Do your theory test (just over £20)
Do your A2 Test,
Most people do the first and last parts as part of an intensive course, which depending on how many days tuition (4-6 usually) can cost anywhere from £450 to £600,
Once you have the A2 licence that is a full licence with the exception that you are restricted to 33bhp for the first two years, but you can carry pillion passengers and go on the motorway,
you'd then obviously need to get the gear which would be £500+ really, and the bike and insurance.