As someone who is also new to the ELR/Tactical Marksmanship world, I think I understand what you are asking. When I first started researching "putting together a rig" the more I read the more complicated it became and the more confusing as well. The dozens of different cartridge types, ballistics information, twist rates, optics, the various rifles, and hundreds of opposing opinions etc.. drove me crazy. So I understand when you say you aren't exactly sure.
Since you only seem to have a few criteria. First be able to accurately shoot to 600yds, readily available ammo at a decent price, and all for around $1000.00. This is would be my suggestion for a budget precision rifle configuration,
For your Cartridge the 6.5 Creedmoor. Reasons being, the external ballistics excel even out past 1000yds, where the .308 and .223 would not. The assumption here that if you do well at 600yds then later on you will want to move up to 1000yds. Anyway, this is not to say that plenty of people don't ding targets at 1000yds with a .308 because they do, but from what I can tell they have tinker a lot with their loads, chassis, barrels etc.. to make this happen. And I assuming you do not want to load your own ammunition at this point and would simply like a more out of the box solution. Moreover, the 6.5 Creedmoor is pretty straightforward when it comes to Ammo because from what I have read Hornady makes quality factory ammo that is readily available plus reasonably priced. The 129gr SST SuperPerfomance or the 120gr GMX come to mind. In addition, it has less kick than a 7mm round, if recoil is a consideration which it was for me.
For a rifle the Savage11. Many believe Savage Rifles are a great rifles for 1st time shooters and I agree. They are supposedly highly accurate right out of the box, have a lot of aftermarket support, are easy to tinker with so you can do things like free floating the barrel and other mods to assist with rifle harmonics and accuracy, have a good customer support and are surrounded by vibrant online communities to help answer questions for new people like me!!
As for Optics, the SWFA 10x Fixed Scope for the $399 is the way to go. The 10x should get you out the 800yds I would think, but if you get to much further out you will probably need to move to a variable such as Vortex, Steiner, Nightforce etc..
Personally, I decided against a bipod to start and purchased two gun bags instead from str8lacedgungear.
Here is the cost
Savage 11-$470.00
SWFA 10x-$399.00
Rail and Rings-$60.00
Gun Bags-$95.00
Tab Gear Sling-$68.00
Triad Stock Pack=$37.00
Total-$1129.00
You still have shipping and maybe taxes but it is close!!
Please take what I say and double check, and I welcome any corrections to any misinformation I may have given from more the experienced shooters here. As I said I am very new to this and don't want to mislead anyone through my own ignorance.
Hope this helps
Regards