At this point in time, everyone wants to shoot to 1,000, and then a mile. That is good and bad, but there is a lot of good budget gear out there.
With the right twist and bullets, .223 can go to 1K all day. My best 10 shot group at 1K is just over 8" for 10 rounds (the gun is not optimized for shooting LR), which is better than my best .308 group at 9.8".
The faster the bullet, the less wind, the easier it is. I shoot a lot of .243Win and .260Rem at the longer distances (600+). High BC 6mm and 6.5mm cartridges (there are at least 15 of them that work) are some of the easiest cartridges to get to 1000 with some being able to stretch out to maybe 1500. Of course we are talking about target shooting, not hunting. 6-8" 10 shot groups are certainly attainable with the right gear.
Some people like the Chassis systems (Ruger, Savage, Winchester, Tikka, SIG, etc. make factory ARish or chassis/modular systems) which I recommend for newer shooters. It is easier to adjust fit and such and if you do it wrong, a skilled shooter can help you get it fit. Some hate Chassis and want a more conventional stock. The new Rem MagPul, Savage, Tikka, etc. make target stocked rigs with adjustable cheek risers. Then you have the fixed stocks which some like and are more suited to hunting. Some guys like Howa actions to drop into a custom stock as well.
Lots of choices for sure, so get to a local LR match and check them out. There are differences in quality and accuracy for sure. Twist rate is huge...you want a twist rate that will stabilize the heavier bullets for the caliber so they are stable out at 1000 yards. There are barrels that will shoot lights out at 100 yards but fall apart mid-range (400-700) and that won't work.
Glass: SWFA SS series for budget (300-500) and Burris XTRII line to step up into the mid-range (800-1500). If you can go past 1600, there are a lot of good choices.