- Don't start this with a gas gun, especially a large-format AR (.308. 6.5CM, etc.). I listen to shooting buddies [b... complain] about their large-format ARs all the time. They can be capable of great accuracy but are FAR more finicky than bolt guns. I started precision rifle with a DMR-variant AR with a good barrel that would hold about 1MOA at 100 yards with decent .223 ammo - I had the rifle BEFORE I got interested in long-range. That rifle is gone, traded for a .223 bolt gun to go with my 6.5CM "big rifle."
- Scope: Higher-end scopes tend to be more repeatable (with a 100-yard zero, you turn the turret almost 2x revolutions for 1000 yards. Will it go to that point, and back to your zero, and back to some other range setting, time after time after time, for years, in the dust and heat, under recoil? If you don't shoot that much, and don't plan to formally compete much if at all, and won't dial in new settings much, a $400-800 will probably be fine. Otherwise, I'd say $1000 should be your starting point. I learned this lesson the expensive way. Cheap scopes -> less cheap scopes -> midrange scopes -> decent scope -> still want to upgrade to $2500 range.
I'm going to have to disagree with the AR thing. My first really accurate rifle was an LR308 clone that I built myself. I broke in the barrel and sighted it in at 100 yards and imediately went to 1,000 yards from there. With my best group at that distance around 6". Not too bad for a long range noob.
I had some minor parts compatibility issues during the build but since it has been complete the only finicky thing has been adjusting the gas block when I change ammo. I should probably just open it up another notch or two but I like the way it runs when the gas is turned down to the minimum.
As for scopes, price is a poor way to judge quality. If you are looking for a great value, your scope is probably going to be coming from Asia. The really cheap stuff comes from China, the Philippines seem to be improving but their best seems to be mid-range. Japan seems to do pretty much anything.
It's getting to the point where scopes are like white box laptop computers. There are only a handful of makers and they only have a handful of basic scope designs but they make those designs with various options and cosmetics to fill out the product lineup of many brands.
The optical company making most high end Japanese scopes is Light Optics Works (LOW). They make Vortex Razor, Athlon Chronus, Bushnell's high end tactical models, Nightforce and others. If you can find a LOW made scope, chances are the mechanicals are going to be fine and if it is a model known for having good glass, it should be a nice scope.
I have bought three LOW made scopes recently. Two were Bushnell LRHSi 4.5-18x44 from GAP for $750. Very nice glass, built on a 30mm tube, plenty of internal adjustment for 1,000 yards, might have trouble getting to a mile. It's FFP, Mil-Mil, illuminated x-mas tree reticle with a zero stop. One of them had the elevation marking slightly off center so I'm doing a warranty exchange for a similar LRTSi which has a different reticle and pull up locking turrets (LRHSi has a plain target turret for elevation and a capped windage turret). The reason for the return is cosmetic but I want to try the LRTSi so I'm happy.
The other is a Tract Toric HD 4-20x50 which was more expensive but it's a 5x erector compared to 4x on the Bushnell scopes, it has the pop up locking turrets like the LRTSi and the glass used is made by Schott.
All three of the scopes seem to share common origins, the turret looks the same while the tube and bells are different on the Toric due to the different optical design.
They are all high end scopes despite the fact that they cost 40-60% of the 34mm tube competition (Athlon Chronus) and they seem even cheaper compared to European or American made options.
Any of them would be perfectly suited on an entry level gun and not too out of place on a higher budget build.
If you decide to upgrade later on, they will make really great hand-me-down scopes too.