A 223 will go that far with the right bullets (77gr), but something in the 243-308 size class (243, 260, 7mm-08, 308) is more than enough for target and punching paper.
And if you're on the cheap, Savage is perfect.
I don't know what you're smoking, but a 77gr bullet might *BARELY* shoot minute of mattress @ 1000yards....and thats if there's virtually NO wind.
for 1k and a .223, you're talking a MINIMUM of an 80gr hybrid/VLD type bullet (like a sierra 80SMK, or Berger 80.5fullbore, berger 82HPBT, etc)....and if you have any hope of them staying supersonic (at least at sea level), they're leaving the barrel @ 2900fps (which isn't possible *safely* with anything shy of 26"). I'll dig this post up mid summer and update with my results...i'll be in Colonie NY after Perry this year to shoot 1k, and I'm gonna give it a go with some Berger 90's in a 1:6.5twist kreiger in my service rifle for one of my strings. i'm not optimistic about it though.
why is it that everyone looks @ 1000yards as some sort of monster goal? If you wanna shoot 1k, and don't have a proper rifle, hang around at the local rifle clubs. gun folks (as a rule) LOVE to show off their toys, and share their knowledge...and knowledge is a good thing to have when you're shooting @ extended ranges. don't know a come up? guess wrong? could send a bullet into the dirt and waste ammo trying to find a trace....or worse, lose it right over a berm and into a populated area.
you want a cheap, easy, (probably) MOA or better 1000yard gun. it REALLY doesn't exist. if you want something that'll reliably make good hits @ 1k (assuming you're doing your part), is isn't gonna be "cheap", and the ammunition (should be reloads) is going to take some real care to get right (my LR .308 ammo (Sierra 2156, 155gr) for my palma gun leaves the barrel right @ 3000FPS, ES of 6, SD of 3. that was "acceptable" for 1k. SD's of 10+fps? ES's of 20+? you're gonna see some significant vertical stringing on target.
evaluate exactly what you want for a rifle...then build it. you're better off taking your time and doing it right than trying to cheap out and end up with someone that's only going to frustrate you.