I've just taken delivery and fired my .308 10FP. Only had time for two bona fide 5-shot groups after the all-day break-in process. .292" and .612" (without the single flier I threw it was a 4-shot group of .247") at 100yd.
I doubt very much if an OEM Remington 700 in any configuration or price can match that out of the box.
Accuracy at long ranges can suffer from short barrels--I wouldn't suggest a 20" Rem 700 for 1000yd, but at 300 yd, almost any length will do fine. The general rule (as I recall) is, for every inch lost, 50fps is lost in muzzle velocity.
If your wife is adamant about "explosives" in the home, I think you're relegated to .223, because it's cheaper to purchase (no way you're getting to 800yd though). If reloading is an option, and 800yd is the goal, I'd go .308, and if limits are ~$700, I'd choose some version of the Savage 10.
For rifle-reloading tooling up, I'd set aside $350 for everything, (scale, dies, ammo components, measuring tools, books, tumbler, etc.) based on a Rockchucker as your press. That's just a WAG for an estimate, but that's provided nothing you buy is junk, and you never buy 'up' to replace your initial purchases with better equipment i. e., better calipers, micrometer, scale, etc. You can do this for way less with a rudimentary Lee hand set (say $100 for everything less press and measuring tools), but they'll not be near 'accuracy' grade, nor time-efficient. You can save big bucks buying RCBS equipment as used (ala EBay). All of it is lifetime guaranteed except electronics, and that ploy can sometimes save up to 50%.
One thing no one's mentioned--a generally accepted axiom among serious riflemen is 'spend as much on the optics as you did on the rifle (at least)'. If you can't see it, you can't shoot it, and there ain't no miracle cure for 800 yard mirage from Simmons, Bushnell, Trashco and the like. Leupold is entry level for > 600yd, and some would say Leupold is entry level for any target at any distance, if one is serious. Burris is in my opinion, a better optic for less money.