First off, sniper=the person, sniper rifle=the gun.
Airsoft GI is a retailer...what is the brand on those parts? If it doesn't list one, I would suggest you get something by laylax, PDI, or EdGI for those parts.
My personal upgrade path on my vsr-10 is:
TF sleeve/bucking combo by Noobie
TDC adjuster kit by Noobie
EdGI ported 6.01/435 mm inner barrel
Polar star piston
EdGI cylinder head
laylax teflon cylinder
Laylax ball bearing spring guide
M-trigger by Noobie
Both EdGI and Noobie are players that manufacture parts, and the build quality and design is by all accounts much better than the major manufacturers. The TF sleeve/bucking and TDC adjuster kit basically change your stock HU chamber, and have been very consistent in all tests so far. Highly recommended (if you go this route, you won't need the Nineball bucking)
I didn't include the spring in that list because that's based entirely on your playing preference. Due to minimum engagements and fps regulations on most airsoft fields, your fps depends on your playstyle. Add an sp170 (in addition to the sp130) in case you end up going for a higher fps. Springs are cheap.
This also didn't count mods. You'll want to do something to dampen/fill the stock to stop it acting as a soundbox that amplifies the internals. Placing foam around the trigger unit, spacers or cotton around the inner barrel, and cotton in the silencer will all dampen the sound of the rifle. Other than that a very simple mod you can do is to wrap the threads of your cylinder head and barrel/bucking joint with teflon. The teflon tape around the barrel/bucking joint will be obsolete if you go for the TF sleeve/bucking combo, though.
Oh, and personally I'd get the rifle stock and do some tinkering and play a few games with it before you start upgrading, especially b/c this is your first time playing the sniper role. Probably 70% of those who try it decide it isn't for them, and use their rifles as expensive wall-hangers. If you're just getting into the role b/c of your friend this warning goes doubly for you.
You can always upgrade after a couple games if you feel like you like the role but need better tools for it. A stock bar-10 is quite decent if you clean everything up and fix compression issues, anyway. You'll be fine w/o upgrading it immediately.