First of all you need your provisional license (it will be valid for bikes and cars) which costs around £50 and can be applied for online or at your local post office.
Once you have your provisional, you then need to do your CBT (Compulsory Basic Training), which is basically just a day’s course (not a test). The price of a CBT can vary widely so make sure you check out the prices at several motorcycle training companies. For details visit this website.
Once you have a provisional license and CBT, you are permitted to ride a motorcycle/scooter up to 125cc, unsupervised, but you must display L plates and you cannot carry passengers or ride on motorways.
To be able to remove your L plates, carry passengers, ride on motorways and ride bigger bikes, you will need to do your full motorcycle test (theory and practical). For details visit this website.
I would suggest getting your provisional license + CBT and buying a 125cc bike to ride around on for a while as a learner, then when you are used to it, book your test.
You're making a good choice choosing a motorcycle - it will work out a lot cheaper than a car.