One of the first things you will need to find out is whether your city/county zoning permits you to operate a "gun shop" from your home. If you live in a restricted neighborhood, that could be an issue as well - in that case you will need to check your Declaration of Covenants and Restrictions.
Most likely you won't be able to use your home address as your place of business and do business elsewhere as a gun shop without obtaining the necessary local licenses there as well. Also, I believe your transfer log and firearms need to be located on the site of your gun shop in the event BATFE wants to do an inspection.
The bottom line - if you can legally run a hair salon or used car lot from your home, and State laws permitting, you shouldn't have any problem.