Once you receive the new Hub and plug it in - it should get you connected right away. However it may take an hour or so if the hub needs a firmware update and then be fine. If it still isnt connected then - sometimes the Hub has not been activated onto the new account correctly - a phone call should get that sorted - although it may then become an "overnight" update.
Your day one billing date... is from the moment you first connect to the VM Network on the new hub.
They probably changed delivery date to give time for the old account details be erased from the database on Oct 2nd before your new details can be added for an Oct 3d start. - I think that update gets run overnight for their computer.
Be aware - sometimes (see threads on here) VM get their dates crossed and the connection goes dead earlier than the agreed date - watch out for that and if it happens try and move your connection forward.
You should get a better deal as "new customers" - try the sales team on 0800 183 1234 but see what the best deals are on offer on their website before agreeing to anything.