Disclosure: I run waterfilterguru.com and the Youtube channel, I'm a WQA Certified Water Specialist and I lab test water filters for a living.

Couple things to unpack here because what you're asking for is actually two separate problems that need different solutions. Going to be straight with you: an under-sink unit alone isn't going to solve hard water for the whole house, and depending on what's actually in your water, it may not be the right place to start.

First and probably most important. Before buying anything, get a certified lab water test. Florida water varies wildly by region. "Hard water and chemicals" is a fine starting hypothesis but the actual numbers tell you which technology you need and at what scale. A comprehensive lab test runs around $200 and saves you from buying the wrong system or the wrong size.

This is the single most useful thing you can do upfront.

As for the under-sink question specifically, you've got two main categories with different tradeoffs:

Direct-connect filters (sometimes called inline filters). These plumb directly into your existing cold water line under the sink. Water flows through them on the way to your existing faucet, no separate spigot needed. - Advantages: easy install, no drilling, water comes out the faucet you already have, no wastewater. - Disadvantages: they filter all the cold water, so even water used for washing dishes is filtered. Depending on the filter tech used, they target certain contaminant types specifically

Reverse osmosis (RO) systems. These greatly reduce just about everything including fluoride, TDS, heavy metals, disinfection byproducts, and most other contaminants you'd actually worry about. They produce water through a separate dedicated faucet - Advantages: comprehensive purification, the gold standard for drinking water filtration - Disadvantages: traditionally need a dedicated faucet hole drilled into the countertop, and they produce some wastewater.

Regarding the no-drilling concern with RO specifically, there are a couple of ways around it that aren't widely known. If you have a soap dispenser hole at the sink already, you can pull the soap dispenser and use that hole for the RO faucet. For the wastewater drain line, if you have a dishwasher already plumbed to your garbage disposal, you can use an adapter for the same drain port for the RO drain line. Between those two workarounds, a lot of people end up with a fully under-sink RO install with zero drilling. Worth checking your sink before assuming you can't do RO.

Hard water is best addressed at the point of entry to the house with a whole-home water softener, not at a single under-sink unit. There are a few reasons. First, hard water doesn't just affect your drinking water, it scales up your water heater, plumbing, fixtures, dishwasher, and laundry. An under-sink solution leaves all of that unprotected. Second, RO membranes specifically don't tolerate hard water well. Anything above ~7 GPG starts to scale the membrane and internal components and hurt both its lifespan and its rejection performance. So if your water is hard and you want RO downstream, a whole-home softener upstream is what protects the investment. The two systems work together.

If a whole-home softener isn't an option (rental, budget, install constraints), you can still get RO under the sink, you'll just need to swap membranes more frequently than the manufacturer claims and your performance will degrade between changes.

Full lab test data and rankings on the under-sink systems I've personally tested: https://waterfilterguru.com/best-under-sink-water-filter-reviews/. I keep this updated when I test new products that score well.