Personalised driving reg

You can only buy plates the DVLA have already issued and that are not in use, you can search their database Here , you can buy plates from other companies than the DVLA but they all use the same database.
Generally the shorter the plate or the closer it is to a name or word the more it will cost, like 'JOE' prob costs 50k+, you'll need to pay to 'register' the plate to your vehicle too (£150 ish?) and that gives you the paper work you can take to somewhere that physically makes plates (like Halfords) and get the plates themselves.

I believe that some companies that handle registration sales have their own stock of numbers they've bought from previous owners (it's possible to transfer a number onto a certificate -- it doesn't need to be assigned to a vehicle). The same companies will happily sell you a number that you could get direct from DVLA -- but obviously will add their own mark-up on top of what DVLA charges.
One thing for the OP to be aware of -- you can't put a personalised plate on a vehicle that would make the vehicle look newer than it is.