You should be ok with ADSL. If you have a BT phoneline in the house deactivated BT can usually activate it almost immediately and you can order ADSL the following day.
All things being well with the line test you should be online in 5-10 working days depending on when the next run of activations on the exchange are due (BT don't do them piecemeal they are done in bulk so it's a case of which batch you are on).
You won't have to pay a migration fee at all as you aren't migrating from one DSL provider to another.
You will have to pay an activation fee unless ISPs have special offers. This fee is currently £58.75 (£50+VA T). This does
not cover the line test, that is free, and does
not cover first month's rental fee. That is the price BT charge the ISPs and most charge at cost.
For info about ISPs from real users check out
http://www.adslguide.org.uk and their forums
http://bbs.adslguide.org.uk
If you went with an ADSL ISP and ordered now you'd be set up before the end of this month.
The rest is as DrAwesome says really.
Last question, why are you considering dropping ntl bb? Cost I'm guessing.
Thanks and if you move I hope it all goes smoothly and your new ISP serves you well - metronet and plusnet are both very well regarded
