The regulations on alcohol sales vary widely by state AND city or county, so the issue is rather complex. You will discover that states, cities, and counties regulate the types of alcohol that may be sold (beer, wine, liquor, etc.), permitted alcohol levels (including perecentage of alcohol in beer and the sale of reduced alcohol in some spirits), establishments permitted to sell certain alcohol classes as well as minimum/maximum quantity purchase requirements and whether the product can be sold only "hot" or chilled, hours and days of sale limitations, etc. OK, so that was not much help.
I will address as best as I am able some of the issues of retail (or package) sales as opposed to the rules regarding on premises sales and consumption, which is a different animal altogether. The easy part is as you are already aware some places are wet or partially wet while others are (bone) dry. In most states it is left up to local governments whether counties and/or cities permit retail alcohol sale AND what types of alcohol are sold there. So you will find some places, especially in the South where no alcohol is sold legally at retail, while others permit the sale of some combination of beer, wine, and/or liquor. It just varies and it is better to make inquiries about any particular place in which you have an interest. Most Florida communities have alcohol easily available, as do many parts of Georgia and other Southern states. If you don't find it right where you are you can usually get it within a reasonable distance except in a few states.
Some US states/cities/counties permit the sale of all types of alcohol in grocery stores and/or pharmacies, while other permit sales in attached or satellite facilities. Some permit only sales of beer and wines (no liquor) in grocery stores and pharmacies. Still others permit the sale of diluted spirits...such as reduced alcohol vodka in grocery stores while restricting full-strength products to traditional, i.e, standalone liquor retailers. Some locales permit all types of alcohol sales yet prohibit ANY sales at grocery stores or pharmacies. A number of states still operate govenment-owned (or franchised) retail outlets fo alcohol sales. These facilities have the franchise for selling all (or some) of the permitted products in their area. State stores might sell liquor while non-state stores might be permitted to see beer and/or wine. In some states and cities, if you want to buy beer, you have to go to a special retailer or warehouse type operation where you must purchase by the case. If you desire a single or less-than-case purchase you might have to go to a pouring establishment and purchase it over the counter at the bar at typically inflated prices. Many locales that permit retail beer and wine allow the purchase of individual containers and multipacks at convenience stores. In many (maybe most) states, all alcohol sales are by private retailers, licensed by the state and local governments involved. In any event, the actual days and times permitted for retail sales will vary widely. Some states prohibit ALL Sunday retail alcohol sales while in others it is left up to the county and city governments. Sales on certain holidays and other special days might also be restricted. You will discover that in some areas retail sales of some or all alcohol are shut off before midnight, while in others some or all alcohol might be allowed until midnight, 1 AM, or even later. Some areas might have no hour restrictions at all.
Some states, cities, and counties have rules on the legal maximum alcohol percentage in beer and wine. That limits the availability of certain products, especially imports. Still others have restrictions on brewpubs and microbreweries. On top of it all, oftentimes it is technically illegal to transport alcohol from one jurisdiction to another in many cases because of tax issues (alcohol taxes are NOT uniform) or because some or all alcohol may be illegal at the intended destination or at any point along the route of transit. This is a holdover from some of the old bootlegging laws, and is sometimes enforced, depending on the politics of the time and the whim of local law enforcement.
Some states permit the purchase of wine via post or package delivery services. Some do not permit this. The benefit is for small wineries whose products might not normall be available widely through traditional distribution channels.
So, did I clear things up?
No, I didn't think so. If anything, I made the waters muddier. So here is what I CAN tell you. I live in Georgia. Statewide there are NOT sales of alcohol permitted on Sunday or Christmas Day at retail ANYWHERE...no liquor, beer, or wine. Most counties are wet to some degree...at least beer and wine. All the larger cities and counties also usually permit liquor sales. MANY smaller rural counties and towns ALSO permit retail sales of liquor. Except in a few areas of the mountains and South Georgia, one does not have to drive far to get beer, wine, OR liquor. All retail outlets for alcohol are privately owned. Liquor is NOT sold in grocery stores or pharmacies. Depending upon the city or county, liquor MIGHT be sold in the same store as beer and wine, whereas in some separate facilities are mandated. In some case the separate facility is merely a door into the adjacent sales area of the same store. Although I'm not sure on this one, I believe the state DOES now permit the purchase by post of some wine from out of state wineries. One is free to purchase less-than-case size beer at retailers, although some locales MIGHT restrict the purchase of chilled individual containers at convenience stores, etc. When it gets close to midnight on Saturdays evening at ALL retail establishments, stores will halt retail sales...some stop even earlier to comply with local laws OR to ensure they do not jeopardize their retail alcohol license.
You brought up one other point. I'm not sure WHAT the legal issues are for importing personal stocks of alcohol from a foreign land. There may be customs excise issues as well as outright prohibitions. I'm sure you can find out more as moving date and destination become clear. Some movers will NOT knowingly transport alcohol...I think more for the risk of getting involved in some smuggling/bootlegging issue as much as anything else. Some might consider it the same as shipping dangerous or flammable liquids.
Hoping that you don't go banging your head against the wall with all this useless information, I wish you luck in your relocation.