.25 MOA is a very high bar. There may be factory rifles here and there that will shoot .25 MOA groups from time to time, but you are very unlikely to acquire a factory rifle that will do that at all, let alone consistently. If you go the custom route, your odds improve, but even a custom rifle
will not guarantee that level of accuracy.
That's the first issue. The second issue is shooter ability. Even from a bench, it takes pretty sound shooting fundamentals to get .25 MOA groups even as close as 100 yards.
With a good rifle that has a quality barrel, good handloads, and decent optics, .5 MOA is doable on a consistent basis. You may be able to better that by a little bit. I have two rifles that will. Neither of them will do .25 MOA though.
You don't need to go crazy with your scope just to shoot at the range. You need decent glass, reliably repeatable adjustments, adjustable parallax, and enough scope adjustment to get you to the 1000 yard mark. A 20 MOA base would also be helpful.
If you are not hunting, I see no reason to go with anything larger than a 7mm. In 7mm, I wouldn't go with a case any larger than the .284 Winchester (but I don't know of any factory rifles so chambered).
Something in the 6.5 or 6mm class would be a better bet. 6.5-284, 6.5x55, .260, 6.5 Creedmore, or 6.5x47 Lapua are all good options in a 6.5mm. The best performing 140g match bullets will require a 1:8 twist. I have a couple of rifles with 1:9 twists that handle 140 VLD's just fine, but that is kind a roll of the dice. 1:8 is a safer choice if you want to shoot the 140's.
As for 6mm, there are many options. Most of the popular benchrest rounds are, to my knowledge, not offered in factory rifles. However, the .243 is a very good option in the 6mm class. Just make sure you pay close attention to twist rate. The best 6mm bullets will require a 1:8 or 1:9 twist.
While you are in the research phase of your project, check out the cartridge guides on 6mmbr.com. There is a lot of useful information there.
As you reach out to extended ranges, you will quickly find that wind and mirage will be the biggest enemy of .5 MOA or smaller groups. That is where the science of riflery transforms into an art.