I live in Florida, have a Florida Driver’s License, Florida Concealed Carry Permit, etc.
If I am in a gun store in another state, Georgia for example, and run across a deal that’s too hard to walk away from, is it legal to pay for it and have it shipped from the Georgia gun shop to a Florida FFL? It seems like it would be because the Florida FFL would do a background check to make the transfer, but I know if it seems logical, it might not be.
Logically speaking! 
It should be. Up to the dealer also.
If you don’t have any limitations with purchasing / owning the firearm in Florida then yes, you can buy wherever you want and have it shipped to your FFL.
I don’t believe you should have any problem with that as long as you have a clean record.
@Gary_H , you just asked a question I have been meaning to ask for quit some time but keep forgetting to ask. 
If you ask the gun shop you are visiting they should be able to advise. I think you would pay at your FFL in your state of residence. However, after shipping, transfer fee, and applicable taxes, it might not be as good of a deal.
Yes, you can buy any firearm you want from an out-of-state FFL. The issues are, if you are not a resident of that state, you can only purchase and take with you rifles and shotguns. If your state of residence has restrictions on what firearms you are “allowed” to possess, then you cannot legally purchase it. If you buy a handgun, it must be shipped to an FFL in your state of residence, where a background check will be done, and then you can have it transferred to you. If you have a home in the other state, and documentation of a physical address in the other state, you can buy whatever you want.
This topic was covered in another thread.
Hey @Dave17 that thread seemed to address dual residence complications, so I honestly didn’t read all the way through it.
Yes you can but you won’t take it home it will nee to be shipped to your local FFL so be prepared to pay for shipping and a handling fee at your local FFL. My advice if you think you might run across the deal of the century make sure your local FFL will do the work, make sure you have there phone # with you since the store you are buying from will need to contact your store and have them send (typically a fax) a copy of their FFL license. Dealers are very careful and do everything they need to feel it’s a legal purchase and transfer. Better for you to if all parties do what they need to do to CYA.
Good point, I will carry a copy of the FFL I have used for internet purchases with me. My son is getting married soon and has developed good relationships with a couple of shops in his area that frequently have unique items available.
I only added the link to that thread as it had links to the ATF site that explained how to purchase firearms in other states. The best advice is to just ask the FFL and as you stated, bring the info for your home state FFL. Just keep cursing the 1968 GCA while you are jumping through these ridiculous hoops.