Just wanted to start out by saying Hello and tell you a little about myself. I'm from WI and grew up hunting just about everything. I joined the military and served my first 5 years at 2/75 in Ft lewis and am now stationed down in Central UT where I have found out that long range hunting and shooting is a way of life. I've spent a great deal of time behind a rifle so I'm not a complete newbie but as far as building a rifle from the ground up I may have some short comings.
So the questions will be asked with a statement of what I want. I would like a rifle to hunt elk sized game and smaller, the cheaper the ammo the better (I don't reload yet) Hunting ranges is a problem due to right now I wouldn't be comfortable with that far of a shot 300-400 yards, but would like the potential to grow in to something further. I shoot vortex optics and have a viper that will be on top of this rifle. Where would you guys start with out breaking the bank $700 for rifle alone. With upgrades to follow.
Thanks for any advice
First, welcome to the addiction and LRH.com. A lot of people here with a lot of knowledge. You are going to be given many suggestions in rifle, but for the price and accuracy, I am and will always suggest a Savage. 300Win Mag will git'er done for ya out to 900+, so for starting out to the ranges you want to start, this would be perfect. The 300WM has many different loads available and some companies (Black Hills, Cor-Bon, HSM, and Hornady) provide premium loads that will give you great bullet selections for your long range hunting needs. Here a few to consider. Don't pay attention to the prices on the website, they are suggested retail, but can be found at lower prices.
My second suggestion would be anything from HOWA, and then the Weatherby Vangaurd (Same action as a HOWA).
"Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it.  But small is the gate and narrow the road that leads to life, and only a few find it.
If you find your self in a fair fight, your tactics suck!- Marine 1st Sergeant Jim Ryfinger
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I would look for a used remington sendero or winchester laredo. With elk on the menu i would go 7mag on the minimum, with the a big 30 falling into the ideal category. Both are upgradable and should shoot fine at the distance specified.
The good and bad news is that there are a lot of options.
Savage and Rem 700 Sendero are very poular in these forums.
Rem - because there are plenty of smiths capable/willing to work on them. You can't say that about all makes/models, even the good ones.
Savage - because you can actually do work such as rebarrel the rifle yourself with excellent results.
Aftermarket parts are widely available for both and good deals are often available on used rifles.
Get you a one-piece 20 MOA picatinny base and a Harris Bipod and you're all set. The only limitation past about 500 yds is going to be the consistency of factory ammo vs handloads. Superformance or one of the others Tank mentioned may give you the consistency needed to reach out farther.
I second liltank's suggestions. I think for the money, the 300 Win Mag is hard to beat for your situation. It will kill big stuff way out there, but won't necessarily break the bank on ammo and the ammo is readily available. I also think the Savage is the way to go. If you compare what you get in the Savage vs the other companies, the Savage is the best bang for the buck. There is only one caliber that I would pick a Remmy over a Savage and that's the factory 338 Lapua Magnums. (will kill WAY out, but ammo is EXPENSIVE!!!)
Some specifics that benefit Savage are the floating bolt head which lends to accuracy, layman changeable bolt head, Accutrigger, the ability to change barrels yourself if you like to tinker in that fashion... Plus, I like the look of the barrel nut. If you throw a picatinny rail on the gun, the nut adds a "tacticool" look and matches the barrel well if your barrel is fluted. I like it, but some don't.
On that note, my brother in law just purchased a 112 BVSS in 300 Win Mag for a good price. The only problem with this gun is it is 10lbs without scope! But, that makes for a more stable platform. PM me for location if you're interested and you can talk to the dealer yourself. He can also get you any of those listed by tank I'm pretty sure.
The only problem with the 111s and 116s is they have the "heavy" Accutrigger. There is the target accutrigger from like 6 oz-6lbs or something like that, the varmint from 1.5-6lbs and the hunting from 2.5-6lbs. But, even at 2.5lbs, that should be good for a hunting rig. Most of my triggers are set to around 3lbs. I have a Remington set a little lower, and a Winchester a little higher, but I wish both were the varmint Accutrigger that the 112 has.
I'm from Wi. also, plus new to this site, but if anybody can get you on the right track, these guys here will. I bought a used 300 Win. mag. for use on the critters your describing, and have far less than $700 in it, it's a model 70 Win., since you have the scope already, their should be several options available, the Savage idea on previous reply is a great choice.
Agree with all the above. But, ask yourself “what is MAX bullet wt. I will ever need in North America”. If it is 185 to 225+ you may want to get a plain old 338WM. I can load down to 160gr and up to 300+gr.
With my limb saver I don't use a break, and mine is only 6.44Lbs.
I have streachability and can learn how to “reach out and touch something” out to 800 < 1000 yds. with plenty of Speed and Takedown power. And, Without buying anything extra, also, ammo is not a $$ problem. Just a thought.
Son, The first shot is the important one - the others just make him run faster! Grandpa 1949 NRA Life Member 1970