It would depend on the size of storage that you need. 50 Gallons? 100 gallons?
How about a large plastic container such as a domestic central heating oil tank (OK, so Florida doesn't need central heating. But wait, something on that line; a plastic chemical storage tank... A plastic septic tank maybe... Bury the container and store the water below ground level. A small electric pump would be enough to service flower/vegi beds...
Along the lines of
here or
here. These may or may not be what you need but its food for thought...
You would have to arrange for overflow when the tank is full - but that would be easy...
When we lived in the New Zealand bush with no services, all our water was collected from the roof and stored in large underground tanks - no evaporation & it was kept cool too.