I shoot competitively quite a lot. I shoot open class bench, stock class bench, and three position metallic silhouette. Will be glad to help you in any way I can. Just a few things to bear in mind, plinking at 300-400 yards is one thing, however once you graduate to 1000 yards and beyond, to be consistently good and competitive, your matches are won and done on the reloading bench.
Consistent ammo is the ticket to success. Powder loads down to the 10th of a grain, and bullet weight just as accurate. Brass trimmed and polished to exact dimensions. It's all very relevant, even matching poder batch numbers to ensure you get the same burn.
Equipment is the second most important thing. For optics, IMHO the March X is hands down the best there is. I use the 8x-80x. I am also a fan of Nightforce optics, neither are cheap but worth the cost to be good.
My Open Class Bench gun is a Shilen Custom, and it shoots like a laser, my preferred long caliber is .338 Lapua, to me nothing is better, especially in timed silhouette competition. You can dial in your 500 yd dope and be good 250-300 yds either side of that easily without re-figuring your dope.
This is the March X looking at 1000 meters taken with my iPhone looking thru the scope. It doesn't get mu better than this. A .25 MOA one click being .125 MOA. Very easily fine tuned. Crystal clear, and fights mirage well.
My Stock Class preference is the Savage 110BA LE, also in .338 Lapua, They come out of the box a nail driver.
AAs I said before the real match is won on the reloading bench, keying on consistency.
I'm a fan or Berger and Barnes Bullets, their tolerances are impeccable.
If you are going to buy box stock ammo, Hornady Custom Match is hard to beat. It's not cheap but it's right. And you get what you pay for. Hornady will custom load anything you want, but you still are taking something someone else has done. A lot of the real enjoyment of shooting happens on the bench.
For NATO Combat Simulation matches I use the DPMS Panther AR-10 .308, that I've tricked out with a Shilen Barrel and Geissele Hi Speed National Match Trigger set, and Magpul furniture.
.308 is a nice intermediate caliber, and works great in NATO matches where you have to shoot NATO calibers. But when you get out around a grand, it's falling off pretty quickly.
From there you just have to burn a lot of brass. Breathing and trigger squeeze is the ticket to being one target all the time. I prefer a light 1.75# trigger. Ed Shilen built me a Wimbleton rifle once that would dial down to 0.5# which is so light, if you shut the bolt to rough it will go off. It had a hydro-shock stock and weighed a ton. Strictly a bench rifle chambered in 7x300 Weatherby Magnum. Extremely flat shooter, but was rough on brass, because of all the necking down. A guy bought it custom dies and all at a match in San Angelo, he wanted it worse than I did.
If you are going to start out box stock, look into the Savage 110 tactical line, they are the best bang for your buck, and USA made, stem to stern. Savage is hard to beat. I'd recommend the .338 Lapua if you are serious about reaching out far, hard to go wrong like that.
300g Bergers OTM hand matched to 0.1g
Lapua Brass, trimmed and polished
92.5g of H1000 pushing 2795 consistently
Winchester LR mag primers