If you're considering SNP, I would keep a close eye on the weather between now and your trip. If we don't see some significant rains, I would think about a different location. The water levels have been very low up until last week when we got 2 days of decent rain but they'll go down again quick. If the water levels hold up, I would consider Big Run and the Rose River. Both have some nice camping spots.
If you do come, I would pick up a book called Trout Fishing in Shenandoah National Park by Harry Murray. It gives detailed descriptions of the streams as well as trail accesses, etc. You can purchase a nice set of maps to the Park here: Shenandoah National Park Association: Maps
. I have the 3 district maps and they are definitely worth it.
The weather will probably be cool at night, so keep in mind that you are not allowed to have a fire in the SNP backcountry. As for the fish, you can expect brookies in the 6" - 10" range mostly with an occassional brown or rainbow mixed in depending on the stream.