We went with the tuft and needle 10" thick, we paid $600 for a queen and love it. It is no sleep number, but for a no frills mattress its great.
We use a box spring but as long as your mattress is not directly on the carpet you will be fine. The matress needs to be able to breathe which is can do on a platform or box spring better than on carpet.
Brand probably doesn't matter to much but foam certainly will, which is why we went with the mattress we did.