I have been thinking about getting my FFL for selling firearms.  However my wife doesn't want people coming to the house for transfers and such.  I am assuming that I will need a storefront to put under my FFL, is that correct?

You will need a location for your business premises.  You must keep your records (bound book and 4473) there, and you may only do business there or at a gun show.  I suppose it's possible that you could list your home as the premises (assuming that zoning/HOA permit it), but only do transfers at a gun show.

I'm guessing that she doesn't want people IN the house, am I right?
Is there a way for you to set up a basement shop with its own entrance in your house?
That's what I had at my old location.
What does your local zoning and the lot size of your location allow?
I'm working now out of a finished shed on what is a postage sized lot in a village and doing just fine.
If you aren't planning on having a lot of inventory on display, you shouldn't need a ton of square footage