Thousand yards! Lol. I hunt and I love guns. I think shooting anythinga tthousand yards away can be problematic. My longest shot was an elk at 450~ yards with a 300 wsm. Maybe one of those 50 calibre sniper rifles? Let me know how you do!
God bless

Any recommendations?

By long range, I mean able to hit a man size target at 1,000 yards.

I am still thinking a Savage .308 Model 10.

Savage is a fine maker of rifles for well under a $1000... also, Marlin and Mossberg seem to make fine rifles at comparable prices.

More expensive but still under, or close to, $1000 is Weatherby, Remington, Tikka, Winchester and Ruger. These are excellent makers as well...

A varmint rifle in bolt action usually has a longer and heavier barrel which adds to accuracy, so that is something you might want to consider... nevertheless, in a non-magnum caliber, the 30-06 and .270 are your best cartridges in terms of accuracy and energy at 1000 yards. The .270 is VERY flat shooting, thus accurate, but the 30-06 in a little bit lighter grain than typical 30-06 rounds are very flat shooting, too, yet retain their power at long distances. These accurate, yet powerful, cartridges have some appeal due to their lack of recoil and kick relative to magnum rifles. Btw, the .308 is an EXCELLENT cartridge, too - both accurate and powerful, but it's not quite as accurate at such long distances as the .270  and 30-06.

In a magnum cartridges, the 300 Winchester magnum (or 300 Weatherby magnum) and the 7mm Remington magnum are EXCELLENT cartridges - both very accurate and even more powerful at longer distances. Btw, "Winchester magnum" and "Remington magnum" merely denotes the specific caliber designed and cartridge used, but you can get it, for example, in a Ruger or Savage.... such example is a Ruger 7mm Remington magnum or the Savage 300 Winchester Magnum. Getting a 7mm Mag does not mean you have to get a Remington rifle, rather, you can pretty much get it from any manufacturer.

The military (sniper teams) recently made the transition from .308 caliber to the 300 Winchester magnum, mainly due to the added maximum range of effective kill. The only downside to these magnums is the louder report ("BOOM") and the heavier kick (recoil).

You should be able to find ballistics charts. Winchester has a an excellent comparative chart but you have to download their software to use it.

Savage 110 or Remington 700

Ruger 10/22 is also a great 22lr

Thousand yards huh? Weapon aside, can *you* make that shot? It's pointless to have such a weapon if you can't.

A Savage 30-ought (30-06) is cheap enough, but a .270 has better sectional density than a 30-06, so is a bit more lethal. Neither are really thousand yarders unless you're skilled.

Ammo starts to matter at that range, and a spearpoint has better aerodynamics (but more likely to jam if you have a semi like a Ruger 10/22, but as I already said, that has other problems, like range), so a bolt would be helpful.

A .22 is sure an unlikely killshot of a medium-large mammal, placement would matter. Bigger rounds are a better bet, bigger rounds are also necessary to get a thousand yards.

I'd decrease my range and go with a .45 carbine to plink a large 'mansize' mammal at distance. Followed by a .308 @1000, followed by a .270 or 30-06 @<1000.

In sum:
.308 is your best bet, and can be had under a thousand, but you'll want good optics. You'll need a prone shot, and a stable barrel (sandbags). 7MM probably don't come less than a grand :), or as I said, get closer with a .45 carbine :)

Wow, zombie thread! To the main point, a thousand yards seems a little unrealistic. At that range, I think accuracy depends a lot more on the shooter than on the rifle itself. I'd certainly not go lighter than a .308, and even then I don't know how well it would do at that range. Not that I'm an expert by any means, but at that range you'd probably be better off with a .338 Lapua Magnum or a .50 BMG.
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By the way, what on earth do you want to shoot at such a range, anyway??!!

If the shooter is capable, the .308 is capable of 1,000 yds. As Kazamierz notes, the omnipresence of the .308 is an advantage—even over ballistically superior cartridges.

I don't like the new format at Sniper's Hide (firearms, optics, and accessories used to have separate threads), but, compared to gunbroker.com, there is a much higher percentage of excellent used equipment for sale here: https://www.snipershide.com/shooting/forums/firearms-buy-sell-trade/

While I wouldn't dream of buying a recently manufactured Remington 700, older 700's and any of the high end actions that share the Rem 700 footprint are good choices.

I think very highly of the Desert Tech SRSA2.  It has the advantage of being a bullpup configuration bolt-action with return-to-zero 20-second barrel conversions. You can shoot multiple cartridges without having to put a high-end optic on every single one, a huge cost saving if you shoot multiple cartridges from .223 to .338 Lapua. I have gotten ⅛ moa groups from a bench with the 6.5 Creedmoor barrel and our most perfect reloads.

http://deserttech.com/srs.php