I was in the water from day 8 onward...our son was in the water as soon as I stopped bleeding enough to go in myself (I think maybe a couple weeks?)
Back in the day it was cloth diapers with the plastic/rubber thing over it. The little swimmers work fantastic. If they're too big though, you can always go old school. Do NOT use a regular diaper...the gels absorb and explode the diaper, polluting the pool and risking major damage to the filter.
While this young, they DO still have the reflex that if you blow in their face they hold their breath (hence the whole 'baby swimming underwater' thing. We never did that, but I know many families who do.
Have fun! The family pool thing is great, soooooo much less chlorine for little eyes than a public pool or splash pool.
As for wearing...little baby rashguards (too cute) can protect from the sun. We just always went in naked/or with just a diaper until one-ish.