Advice & Tips:
The doctor who did my son's neuropsych evaluation recommended swimming as a very good activity for patients with autism spectrum disorders (because the body always needs to be doing something, it is great for sensory regulation). I had already taken my son to the local hotel pool a couple times and he liked it, so we got a monthly pass ($65 for family of up to 5).
On the second weekend, he was already starting to let go of me for a second or two to tread water. He was proud he could do it on his own. This past weekend, about a month into starting to swim regularly, he let go and even swam (doggie paddle) halfway across the pool himself. Three times! It was among my prouder moments.
We're going to try to go 2-3 times per week (for 1-2 hours). He really, really enjoys it. I'm not sure what it's doing for general health and his ASD yet, but it's great for confidence and exercise, if nothing else.
If there are any downsides, it is that I'm not comfortable with the amount of chemicals in a public pool like this one. I take my son and often my older daughter by myself, so afterwards I take them into the men's locker room. I try to time it so there will be nobody else in there. I run the shower for them and they have a fun time running around under it as I try to rinse away some chemicals. I know that I'm terribly itchy after swimming (granted, I don't rinse off as much as them), but they don't seem to have that issue yet. I'm keeping an eye on it though.