Welcome to FL!
I also have a water softener, and even a
reverse osmosis unit. I use
RO (extremely soft) water in my tank, and a little hard water from the outside tap. In my 30 gallon tank, I have about 5 gallons of the outside water, rest is soft. It's been fine for my fish.
I think most fish will adapt pretty well to your water, especially if you do a mix of the water like I have. Once you choose your fish, I'd like to recommend you post them on our forum, and people here are happy to give you suggestions on compatibility, size, etc.
I notice that you don't know about the
nitrogen cycle - this is key to keeping healthy, happy fish. You should read up on it before adding fish to your tank. Also, there are ways to cycle your tank without using fish.