Florida's Liquor Laws vary from county to county and city by city. Over all its safer to buy liquor before Sunday, as it is not available before noon, except in Miami. Liquor and beer/wine are sold at different locations. You can pick up beer/wine at a grocery store or gas station. Liquor must go through a state authorized retailer. Most liquor stores close before 11pm.
Go to an "ABC Liquor" for spirits, during the daylight hours except on Sunday.
Publix or a gas station (I don't understand that--that's illegal here. Doesn't that encourage you to drink and drive?) is the place to get beer and wine, up until 2am.
Don't plan on partying it up at the bar past 2am.