I know that I want a PRI full length tube, ARMS SPR full length rail, LMT upper receiver with a ARMS #40l rear sight, and a RRA arms enhanced bolt and carrier.  What kind of barrel do I need and what kind of flash suppressor and front sight?  I like the GG&G front sight, but it is expensive. What kind of optics?  I have seen a lot of these with Leupold scopes.

It sounds like you're wanting a Mk12 Mod0. I'll give you the specifics for the military model since so many guys are building "SPR's" and they aren't exactly like the rifle the military developed.
 You've got the PRI tube and ARMS rail covered. Don't forget the PRI flip up front sight a standard ARMS #40 rear sight, and an Ops Inc style muzzle brake and collar. For optics, you'll need ARMS #22M (medium) rings and a Leupold VariX III or MkIV 3.5-10x40-preferably illuminated and with M3 knobs. The Leupold MR/T would be good too, but Midway is currently getting rid of their VariX III 3.5-10x40 w/ M3 knobs for $599.00, so it would be cheaper. If you don't go with the PRI Gas Buster charging handlae, at least get their military "big latch" to give you the look.
For a barrel, contact White Oak Armament and get their SPR contour barrel or Adco Firearms, who sells the WOA SPR barrels.

I built mine not feeling a need for an EXACT clone. Here is what I built....

Specs:
RRA Lower + LPK
WOA A4 Upper
WOA Stainless 18" 1/7 SPR Barrel KG Koted black
WOA Bolt Carrier group
Phantom 5C2 Supressor/Comp ($22 vs $100 for Ops Inc)
PRI Gen 3 Carbon Fiber handguard
ARMS #38SPR PEQ2-3 top rail
YHM Flip up front site/Gas block  ($80 vs $180 for PRI0
ARMS #40L Rear BUIS (*Thanks to Gun Gallery)
DPMS Panther grip
ARMS Harris bipod mount + Harris bipod
A2 Buttstock

Still waiting to get my ARMS #22 rings for my ATN 5x33 scope.

I saved quite a bit of money on items that were "functionally" the same.
I'm not a scope snob. While I appreciate Leoupold quality, it's not a must have.
(That is a BSA 4-16x40 Illuminated Mil-dot scope I had in the safe.)
Most of my parts came from ADCO.
The rifle looks and shoots fantastic!