"I just got an FNAR (7.62 NATO) rifle and am looking to scope it up. I am not a thousand-yard shooter, more realistically 300-500 yards (I only have access to a 300 yard range anyway)."
The FNAR tactical / sniper rifle was first introduced to shooting, public in 2008. It is a product of the famous Belgian company FN Herstal - Fabrique Nationale.
The FNAR rifle is based on the popular FN / Browning BAR hunting rifle (no relation to the original Browning BAR M1918 rifle of World War II fame).
"Any advice on a good scope? The FNAR has Picatinny rails for the mounts."
My advice: In most cases a good scope will cost more than the gun, for the money a Leupold is hard to beat. I recommend the Leupold Mark 4 LRT 3.5 X 10. This is a Long Range Tactical scope - the difference between this and a hunting scope is the tactical scope has ballistic compensation on the turret so you can adjust for range without having to unscrew the elevation knobs and break out the screwdrivers.
"Is this fairly easy to scope up myself if I order 30 mm Picatinny scope mounts? Or should I have a gunsmith mount it up?
How would you recommend initial sighting? I have seen these bore lasers, but they seemed to be a bit gimmicky, and I didn’t see how they would really reflect well at distance.
Also, where should I sight in order to use the mil dots for elevation – 100 yards?"
You ought to be able to slap that scope on yourself no problem - it doesn't take a gunsmith, it is a simple operation you could do on the countertop at a gunshop, or anywhere for that matter. A trick with the Pickatinny rails: when you're pulling one optic off and slapping another on as mission changes (what the rails are designed for) - mark the side of the rail with a bit of paint so you always remember where your scope goes.
The bore lasers work. I once zeroed a USN Mark 12 Mod 0 SPR with a bore laser over 30 meters in a hanger because there was no testfire range available then took it out on mission and hit centermass at 300 meters. I would still prefer to zero on a range, any day.
Zero your optics for 300 meters and you'll be good for lesser distances. The technical data for ballistics (characteristics of climb, etc) should be in the literature for the weapon. Generally, the round climbs and then drops down, crossing the line of sight twice (once on the way up, at about 50 meters, and then going down, at about 450 meters).
Then you will be ready for the belltower.