I do some 500 yard and in shooting, mostly in the 100-300 yard range. I do it primarily with a Savage 18" barreled .308 action that I dropped into a an XLR Industries Element Chassis and topped off with an inexpensive but solid Primary Arms 4-14 FFP scope. I’m still trying to decide what ammunition to feed it. So far, 175 gr federal gold medal match is grouping about half MOA if I do my part. It’s a great rifle, and I don’t regret going with the 18" barrel. In fact, I am glad I did, since the lower velocities mean I am learning to deal with wind and other speed bumps that arise at long range, and that was the point of building an inexpensive but nice long distance rifle.
Savage:
http://www.budsgunshop.com/catalog/product_info.php/products_id/716008440/Savage+P-SR+308+18+HVY+THR+BLK
XLR Element Chassis:
https://xlrindustries.com/collections/chassis/products/element-chassis
I do some long range shooting with the custom SPR-ish AR15 I built for myself. It isn’t as accurate as the bolt gun, but it does well with heavier bullets so I can ring steel just fine past 300 yards.
I have an inexpensive 16" .357mag/.38spl Rossi levergun that I try to shoot out to 200-300 yards with. My eyesight isn’t all that great, but I am improving slowly and can ring steel out to 200 yards with mediocre .38 special ammo about half the time. .357 extends me out to 300 yards, but I’d probably need better open sights or an optic to really be accurate. I’ll tell you what, though. People typically ignore me when I am shooting the first two rifles I mentioned, but they sure get friendly when the levergun comes out. Everyone loves shooting a levergun.
Finally, I have a Ruger 10/22 that I am considering gutting and accurizing for training purposes. If I don’t, I will eventually buy another one to do that to, since .22lr is finally starting to become available again. I can get 325 rounds of .22lr for about 5-10 bucks more than it costs me for a box of 20 rounds of 175gr gold medal match, and it works just fine inside 200 yards for learning to read the wind, compensating for bullet drop, etc.
I’ll probably start taking classes eventually, but I have been able to accomplish quite a bit drawing on what I was taught in the military, help of more experienced friends who actually attended sniper school or SOTIC, lots of dry firing, and internet forums/youtube.
P.S. - if you have never shot steel targets, you really need to try it. So much fun. If I’m at a range that allows it, I always do a bit of that as relaxation before and after I start trying to shoot small groups.