There are many privately run, rather glitzy (IMO) campgrounds in germany. AFAIK, there is no single, comprehensive database. If you do some web searching, you can find sites like this: http://www.eurocampings.co.uk/en/europe/germany/bavaria/
When we camped in germany last (2004), it was necessary (for us, maybe not for everyone) to select a campground destination in the morning or the night before, and not rely on blind luck. It's not usually necessary to reserve, although in popular spots (the campground near Rothenberg is an example) it may be stress-relieving.
I have no FHE with the Czech Republic. Austria is similar to Germany.
When we (three) camped from a rental car, we packed a suitcase with fleece sleeping bags, a 3-person lightweight tent, a CampinGaz-burning backpack stove and lantern, polycarbonate silverware, coffee pot, air matresses (less bulk and way comfy), and sundries of various sorts. When we got to our destination (France in this case) we bought el cheapo sleeping bags at Carrefour or similar hypermarche for like $15, a throw-away foam cooler, some folding chairs, etc. When we were done 5 weeks later, we gave everything to a family we met at the Munich campground.
If money is not in too short supply, I'd buy almost everything after you get your rental car, then you won't have to herc it all over in your packs.
Have you considered renting a VW campervan instead of a car? Take a look here: https://reservierung.drm.de/drm/11fmieta.htm?mfg=A__&PHPSESSID=e209643737360f99189f7b2266cb2c96
There's an agency in Frankfurt (pickup) and Berlin (drop-off). We did this in 2001 and 2004, and it's a great way to be mobile, save at campgrounds, and get a good night's sleep, too!
