Biggest difference between VSR-10 and BAR-10

you also need an AEG barrel for the PDI hop up unit.

By the way, difference's between the two rifles:
BAR10 shoots higher stock.
BAR10 has a much cheaper quality hop up stock.

Get the Tokyo Marui Precision Chamber, it also comes with an inner barrel.
It's just as good as the PDI one.
Also, if you're running a high FPS go for something like Firefly Hard rubber, if you have a low fps go for a soft rubber such as Nineball.

Here, I changed your shopping list to what I think you should get
Laylax VSR-10 Trigger w/ Orange Piston (only if you're shooting above 450fps, otherwise just get new trigger sears and piston sears)
Tokyo Marui Precision Unit and Brass barrel combo
Nineball Bucking (Soft)
Laylax Cylinder Head
Laylax Spring Guide