I visited Lake Anna 2-3 times this summer and enjoyed it every time. The area near "beach" gets pretty crowded in summer, but there are still plenty of areas in the park where it is relatively quite. I normally park near the beach area during the first half of my visit there. After some swimming at the beach, I drive to the other section (Fisherman's trail). That section is not safe for swimming so its relatively quite during summer time as well. There are picnic tables right next to the water. Just like all other state parks in VA, this one also has a parking fees of 5$ and swimming fees of 3$ on the weekends. There are lifeguards on the beach. If you decide to go during summer months and want to enjoy swimming at the beach, just call them and check if the swimming area is open. They tend to close it in case there are any chances of thunderstorms in the area. I was extremely disappointed once, when I found out that the swimming area was closed. BTW, almost next to the real swimming area, you will occasionally see folks swimming in the lake. The only difference is that the other areas are not watched/monitored, and its "free" to swim there (but its "swim at your own risk" in those areas).
There are several marinas offering jet ski / boat rentals in the summer months. I haven't tried that yet, but would be fun to do it on this lake.