Firstly, it's one word Nurburgring.
Factor two tanks of petrol in - at least - to get you from Manchester to the 'Ring if you intend to enjoy the drive.
The ferry from Dover to Calais usually costs around £70, but it depends when you book.
Laps are quite expensive (22e), but the price goes down the more you buy.
Accommodation is as expensive as you want it to be, we found a decent place for fourty-ish Euros a night.
For one of our 4 or 5 day trips I'd be setting aside £500 to make sure I enjoy it but also your car will need to be 110% before you go. I'd advise at least new tyres, new brake pads and a full service.
Four days is better IMO, if you can work it so you get two full days track action. Remember the track isn't open full-time to the public, so check the schedules before you go. Would also be wise to miss big race weekends, but the atmosphere is better then so up to you if you like busy or quiet(ish).
The 'Ring is more of a theme park this year (or so I've heard) and it's a lot more 'touristy'. That means more clubs, bars and hotels