I think the best way to pick an obedience class is to go without your dog and just observe a class to see how it is run. If you like the way the instructor handles the class (both the dogs and the people) then give it a shot.
For my GSD, he has absolutely zero interest in meeting other dogs, in fact he'd vastly prefer they stay far away from him (but he loves playing with my other dog!). Part of that has to do with his history (bad experiences with strange dogs), but I also think some dogs just don't feel the need to expand their social circle. And I would not be shocked if your GSD preferred that your lab kept things less friendly too. This is just a guess on my part, I don't have much multiple dog play experience. Pretty much all of the playing I have observed has been between two dogs.
Niko: American Showline GSD 5 years old
Rosa: American Muppet Dog (GSD/Border Collie mix) 5 years old