I like the rental car in Luxembourg idea. Luxembourg roads are very easy to use, 130 kph on the autoroutes but only 90 in rural areas where you would be driving 100 in Germany or France.
I'd advise getting the most up to date map of Luxembourg because there are always new autoroutes, or parts of them, replacing major roads and your GPS probably won't know about them. Mine never does but I just follow the signs. Because most of Luxembourg is linked by buses (in addition to the (mostly) modern trains) there are plenty of bus lanes prohibited to cars. They are clearly marked but it is worth being prepared.
You will know when you have reached the Belgian border (follow signs for Arlon). Not only do the rest areas with the really cheap fuel and very cheap cigarettes and coffee stop, you see a huge blue Ikea and the road gets worse.
Belgian drivers come with their own "personality", as do Luxembourgers, but driving around Bastogne isn't nearly as much of a challenge as it is nearer Brussels.
To follow up on your interest in Bastogne the car will come in very handy to visit the most excellent and very comprehensive Battle of the Bulge museum in Diekirch, Luxembourg.
You can also see the Patton memorial on the outskirts of Ettelbruck (check my facts on that location, I'm writing from memory) and the American Cemetery near Findel airport where Patton is buried with his men.
All filling stations in Luxembourg have fuel at the very nearly the same price, very cheap relative to all neighboring countries. They are all the same price except a handful which 2 tenths of a cent a litre which is insignificant. Diesel is cheaper and available everywhere, and you get better mileage.
No tolls in Belgium, Luxembourg, Germany or nearby France - the nearest French tolls are at Metz or St Avold.
If you can't find cheap cars in Luxembourg - bet you can - Trier in Germany is just a few miles away down the Mosel.
