If I'm understanding where you're going with your post, it reads for 3 different models. In not up on barrettes models, but the rec7 in 5.56 and the rec7 in 6.8 are probably comparable rifles, but are chambered in different calibers. They are not interchangeable. Some parts are, but the bolt, barrel, and magazines are different.
The flyweight model may designate a light weight version, but like I said I am mot familiar with barrel's line.
As far as any shop getting it, it depends. If your shop is set up directly with barrette, then yes. If not, the. They will need to be part of a buying group that barrett is also a supplier to, such as rsr. Just call your local gun shop and ask if they can get barrett rifles.
Is this your first rifle? First gun?
Eta - milspec beat me..