at one time a 50cc could be ridden on a full uk driving license not sure now, but a 125 you will need a cbt, or you could go for a direct drive which is i think quite expensive. and decide what bike you want gears or twist and go
not sure on prices when our lass got her 125 vesper the shop wouldnt let her drive it out they delivered it to the test centre once passed you can drive on L plates for 2 years before having to do it again but the actual test is 2 parts theory and practical you can get a cd/rom or you can practise online with the theory it costs less than a couple of quid. i passed my bike test 30 years ago this month nothing like it is today
http://www.direct.gov.uk/en/Motoring...ide/DG_4022530
http://www.motorcycle.co.uk/Training.aspx