It's about 400km or so from Calais, all along the E40 for a good while, if I remember correctly. Motorway for 90% except for when you hit the local B roads. To roads most if not all the way are like silk to drive on.
Mid-week is far better than weekends, but many weekdays are booked by companies for testing. It is much more quiet on a monday and especially tuesday. Unfortunately, the Ring taxi may not be on mid-week. Check the offical site for what events are on, although at this time of year everything is finished I think, and ADAC don't have any events but I may be mistaken.
Price was €16 a lap last month (start of October), €56 for 4, and again a little discount for 8. Then it's around €350 or so for a half year pass or €780 (can't remember the exact figure - I am no Ring meister!) for a year.
For the hotel, The Dorint Novotel am Ring is excellent, and very thematic. It's also right next to the ring museum. The weekends can be expensive - Fri Sat Sun can run a few hundred per night, but on the Monday our rate was €128 for two (depends on whether you want to face the Nurburgring starting grid or not). It is around 2-3km from the Nordschleife entrance.
before you go near the Nordschleife, make sure you have checked all essentials (tyres, brakes, etc., ). You are totally responsible for your car - there are no guides, no introductions, no requirements other then roadworthy car and legal license, etc., . It is a public road.
If you go on a weekend, be prepared for lots of closures - if there are bad accidents, they will stop letting people through the tolls until it's clear, might be twenty minutes, might be shut for the day (happened last month when I was there - on the Monday, they shut it at around 1630 - they were peeling bikers from M5s, very scary **** indeed). The weekend was much much busier, as ADAC had some endurance race on, so it was like a car park for the tiny roads around it, parking on local field, etc., .
There is no petrol station there, but there are two nearby - one which is closest does not sell high octane petrol (100 octane, like you get in the other Aral stations).
It is not expensive at all and is a great experience, but can be terrifying if you spin off the track, cross back over it perpendicularly and then 5 seconds later a torrent of bikes and cars misses you by a foot! **** can wrong really really really quickly. Bikers are nuts. Overtaking tour buses is harder then it looks!
I would recommend splashing out on the Ring Taxi (€170 - probably fully booked for months on the weekend, but managed to scab a few seats on a weekeday is easy enough IF the taxi is going on a weekday).
Make sure your car is in top notch condition. Brakes especially and tyres. A few mates didn't get tyres sorted beforehand and had a nasty impromptu meeting with a wall.
Like was said above: it is risky, BUT, you don't have to push it, although it is tempting to.
Oh and cameras are banned in the cars, although they are allowed at the "toll side" entrance.