Sorry, couldn't resist a little humor here.
Sorry, couldn't resist a little humor here.
You can get a Savage bolt action in .30-06 (Model 110, I think) for about $400. Use 220 grain bullets for the elk and 150 grain bullets for deer. Learn to shoot with the iron sights and save yourself a $200 scope. The plus with .30-06 is every little country store around a hunting community will carry ammo.
Boy, now you're in for it. Everyone has his own idea about what makes the best deer rifle.
Remington 700.
Savage 110FP.
high price and low price. I have both and they are both good!
.308 Win or 30-06.
Don't get "overgunned".
It is of course, totally subjective, but for the money you can't beat a remington 700 bolt action. The caliber probably depends on where you hunt and if you plan to do other kinds of hunting with it in the future, but a 30.06 is always a safe choice. Don't skimp on the scope either. Stick with a good brand like Leupold. Get good mounts, too.
These were Remington's least expensive rifles and the story was that the production manager was fired for spending too much money to manufacture them. Production ended around the early 80's.
You can find these in estate sales, classified adds and gun shows. If you don't talk about the firearm much, they are inexpensive. Look for one that appears to be in very good condition.
Accuracy could be expected in the sub one inch and with the right diet, even better. My 78 in 30-06 will put three holes touching each other at 100 yards with handloads. Varmints aren't safe out to 400yds.
I'd recommend a Tikka T3 from Sako. Very accurate rifle. A Leupold Rifleman scope would be an affordable scope. Almost any caliber would work. I have a .270. 30-06 works, too. Comes with a 3 or 4-round detachable magazine depending on caliber. You can also purchase a 5-round detachable magazine. Barrel is free-floating. Single-set triggers are available. Trigger can be adjusted, between 2 and 4 pounds. Set at 3 pounds at factory. Scope mounts included. Drilled and tapped for Weaver-type bases.
check out www.gun-tests.com
A .270 is in that range - a .243 might be a bit light for elk, IMHO, but maybe not. 30/06 is sort of a wonder cartridge but you still have to choose the proper bullet. .308 is roughly the same. 7 mm Remington Magnum will certainly fit the bill if you don't mind a higher-recoil platform - I would NOT recommend a 6-lb rifle in 7mm Rem. Mag. I own one. It hurts, but I'm a bit of a wuss.
You might find something in an older cartridge such as a .257 Roberts (one of my favorite old guns) that could still reach up to elk. There are obviously many more. I wouldn't recommend a 30-30 for elk due to its trajectory but it's a handy little gun in lever action and has probably popped more deer than any other caliber.
Save some money for decent glass. You can do quite well with fixed-power scopes in the 4 to 7 power range but a variable isn't all that much more, and a 2-9 power is usually the limit for the game you're after at the range you're likely to find it.
Avoid the big boomers - they're going to cost a lot of money anyway. There's a lot to be said for popping a .338 Lapua off at a bad guy at 1000 yards, but you're not there yet. .300 Win Mag would be the same story. You'll own one someday...
Try hunting with one of these
My advice? If ya need one, go buy one!
Lando 
Someone mentioned the Swiss K-31. Good choice and excellent value. These can be found for around $100-$125. Another good value in military surplus would be a Turkish Mauser, Model 38. These are plentiful on the online auction sites and can be found in the $75-$125 range. There is a wide variety of very inexpensive surplus 8mm Mauser ammo available for these rifles. One more military surplus rifle to consider is the Mosin Nagant, Model 91/30 or the M-44 carbine. These Russian rifles are a good bargain and are chambered in 7.62x54.
Get an SKS50 with a 50 shot clip :)
Deer?
I was in the same predicament, got lots of advice, and ended up with a fine rifle (Browning A-Bolt .270). But knowing what I know now, most decent bolt-action .270s will kill deer at relevant ranges.
All the main makes of rifles will have quite good out-of-the-box accuracy. Unless you're already a sniper, you'll probably not notice one that is 1/2 inch worse than another. They'll all kill deer very nicely.
The .270 has the advantage of a relatively flat trajectory, while still packing plenty of punch. The .30-06 has the same general configuration and powder load, but it pushes a bigger bullet, so the trajectory is a little loopier. Some of the bigger cartridges being proposed here (.308) are going to hurt your shoulder more, and you'll develop a flinch. They're not necessary for deer, but are excellent for Elk or Terrorists at long distances! ;-)
What I would recommend is to get a .270 bolt action that you like the feel of, and practice practice practice. I suspect you'll be most accurate with a gun that you are happy to use, and do use regularly.
P.S. - Optics can / should cost you almost as much as the rifle. Some people swear you should buy more scope than rifle. I have two scopes, and the better one makes a remarkable difference. It turns dusk into daylight and that's when the critters are on the move!
For some reason, a rifle and scope sell used for about the same as a rifle without a scope. That is why I always remove a scope before I sell one of mine.
Any name brand, Remington, Winchester, Ruger, Browning, Savage, or CZ will be fine. Try to get a common caliber, for instance 30-06, 7MM Remington mag, etc.
It would be a good idea to take someone with you who is knowledgeable but not locked to any one brand.
The Marlin 1895 in 45-70 would be excellent if you don't mind recoil.
I would not recommend any military surplus rifle despite the fact that many of them are great rifles. Most of them are sighted in at something like 300 meters and often mounting a scope is difficult.
I will admit to loving Swedish Mausers, and for that matter any Mauser or 03 Springfield but remember their shortcomings I mentioned.
Ruger Model 77 with a Leupold Vari 3 3x9 scope in either .270, .30-06, or .300 Win Mag ( depending on what yu want to hunt and where ). Ammunition is plentiful.
I also like my model 94 Winchester .30-.30. Great brush gun.
Marlin 30-30. It will sell well if you want to trade up.
If you want more range, a .308 bolt gun from Winchester or Remington.
Remington 700 in .308.
Cheap ammo, very accurate, not expensive.
And oh yeah, it is the basis for the military sniper rifle in .308.