Are you sure the gym pool allows floaties? Most (all?) around here only allow approved life jackets. I would check with the pool before you start buying things.
We also had a plastic one similar to the ones you posted but the edges were too high and DD would launch herself over them. This one has a wide base so she really couldn't pull up on anything to throw herself out of it.
So at 8 months you're going to be there the whole time unless you're talking about a kiddie pool with very little water. I don't think you tubes or rafts. You should be able to just hold her.
My 5 year old swims with nothing and my 3 year is either in a kiddie pool or with an adult.
Most gyms and public pools don't allow flotation devices with the exception of life jackets. At that age, you're better off just holding her and bouncing/splashing around.
Are you sure the gym pool allows floaties? Most (all?) around here only allow approved life jackets. I would check with the pool before you start buying things.
Our local Y is quite strict about what's allowed in the water during free swim time (and during baby swim lessons, FWIW).
Our Y gives access to all the floats, bubbles, puddle jumpers, etc (maybe not the life jackets) during free swim. We always just used theirs. But at 8 months I would just hold her, most people go that route.