A salt water pool is still a chlorine pool. Just a different way of maintaining the chlorine level. Read about that in Pool School.
12x12 or 18x18 pavers will do nicely. The tops of the pavers should be even with the sand bed.
For filtration, easiest to care for is sand, however it does take a bit longer to clear a pool should you ever have problems. Next is cartridge, can be a pain in the tail to clean -- wet messy job. The finest for filtration is DE. Again, read about this in Pool School.
Most likely, your daughter's rash after swimming is due not to chlorine, but to other chemicals and bather waste that hasn't been oxidized. Google "hot tub rash" for a few explanations.
Believe me, Pool School is where you will find a lot of information in answer to your questions.
We here at TFP have a tendency to not put anything in our pools that they don't need. I haven't read of a single case of hot tub rash from anyone that keeps their pool maintained by our methods.
Good luck in your quest for a clean, safe swimming experience for you and your family!