That would probably be a fine rifle, and Savage is another company with a reputation for reasonably priced accurate rifles. You will want a good scope, not a cheap one. A good one to look at would be the SWFA 3-9x42 tactical scope. This scope has a reputation for having very accurate and repeatable turrets, along with good glass a mil dot reticle, and a reasonable price for what you get. Repeatable turrets are very important. Go to SWFA.com.
If you look around you can find a good rifle and scope used. The tactical shooting sites are a good place to find the scope used, and you might find a good rifle on any of the hunting/shooting web sights.
500 yards is not that far once you start to practice and learn some things, and another tool you will need to shoot that far is a rangefinder.
You can find really good ballistic software here on LRH in the G7 Ballistics Calculator, and even factory ballistics information will be close enough to get you started. Just take it into the field, shoot at 5oo, compare the results on paper to what your ballistic print-outs tell you and correct your bullet speed input until the ballistic calculation matches what you got in actual field shooting.
One thing to consider is recoil. It is much easier to shoot accurately if your rifle does not rattle your teeth at every shot. I started out at 14 with an '06 and found the 180 gr. loads I liked kicked hard enough I developed a flinch. Lighter bullet weights, or even better a smaller caliber like the 270, will kill elk just fine and are easier to master. Shoot well first, shoot big and powerful second.