As mentioned layering is key.
Base layer + usual top & bottoms + merino or cashmere sweater/fleece + puffer vest/jacket + waterproof raincoat/jacket.
Wear whichever combo of the above fits the situation. Add gloves, cap and scarf when needed. And wool blend socks.
Uniqlo currently has their packable puffer jackets and vests on sale. They also carry several options of base layers in their Heattech line. I just picked up a couple of merino sweaters on clearance this week for $14.99.
I assume living in Florida you don't want to invest in items you may not wear at home. Sierra is a TJ Maxx brand company. You'll find brands like Columbia, Smartwool, 32 Degrees and Helly Hansen. Like TJ Maxx stores, you need to check back often because the inventory is always changing. My local store currently has more Eddie Bauer waterproof raincoats/jackets in stock than the Eddie Bauer website.