Generally speaking you will only need to get the appropriate general business license for the State and/or city you are operating out of.
If this is a home-based drop-shipping type of business with no other employees you usually don't need anything beyond basic business incorporation paperwork.
I say "generally" because I am describing the scenario where you are selling basic merchandise along the lines of what someone could walk into a normal store and buy. In some cases states may have restrictions on the sale of particular products. In these scenarios you might only be able to sell to licensed individuals, adults, or have to account for products shipped to the state (eg: selling wine into NH).
In the 90's, I operated an ecommerce site that sold burglar alarm panels (among other things) and in some situations I could not sell certain components in certain areas without being licensed and registered myself. But for "standard" things (TV's, etc.) I could sell/ship anywhere in the US with no problem or special registrations.
A "vendors license" is often associated with someone setting up a food or goods retail outlet in a non-permanent location (eg: from a pushcart). Usually all you need for normal operation from the state you operate in is a sales-tax license.
The other good thing I learned early on is to make friends with a local attorney that specializes in small-business incorporation. I paid a laywer ~$400 (in 1996-ish) to handle all the paperwork for my company. I told him what I was going to be doing, and he made sure I had all the right forms and whatnot filed to operate properly.