Excuse my lack of knowledge, but...
Don't be sorry. All the state and federal rules make it quite confusing.
Federal law requires that a handgun purchased out of state be transferred into your possession through a Federal Firearms Licensee (FFL). So you would purchase the gun and it would be shipped to an FFL of your choice. It sounds like you are near Omaha, so I would recommend "RL Moeller Sporting Arms". NFOA board member, and all around good guy. There are plenty others. Generally their fee will be $25-35.
A long gun (shotgun or rifle) does not have this requirement. You could purchase that face-to-face from a FFL in or out of state and take immediate possession. As others have said, it must be a legal firearm in Nebraska (which there aren't many limits).
The other aspect of your purchase question dealing with Sarpy or Douglas counties, I can not answer. Omaha has a handgun registration which others here can answer whether this applies to you.
Sounds like you might be relatively new to firearms or at least handguns. Welcome to the sickness.
Fly