7mm-08 would be a fine elk cartridge that would serve you well. A good 140 gr. Accubond or Partition would do the trick. The .280 Remington is also a very fine cartridge with a little bit more pop.
Thanks everyone for your replies, I've been doing a lot of research and reading your post. Along with the research I remembered my grandfather used a 30-06 when he went elk hunting and have since changed my mind on the 7-08. Still trying to decide what exactly to get but leaning towards a 30-06 or .280 now, more so the 30-06 with sentimental reasons mainly.
I am biased as I have shot a 30-06 for almost 30 years. I have taken around 20 elk cleanly, 1 moose, and a gob of antelope and deer. It is a great round when paired with good bullets. Like any gun, staying within the cartridge capabilities is a must. I set my max range at 500 yards on game (perfect conditions only) but practice to 700 at the range.
Good luck in your decision making- really isn't a wrong choice just need to find a gun you love and spend time at the range.
I always use enough rifle for the game I intend to shoot with it. We all have our limits as to how far we can successfully place the bullet on the killing zone of the animal hunted.
We are "hunters", so accordingly,we use our hunting skills to get to a sure killing distance from the animals.
As others have said, it's a perfectly fine elk round as long as you pick your shots, limit your distance and choose a well made bullet. My hunting partner uses a Rocky Mountain rifle in 7mm-08, but won't take a shot over 350. Seen several bulls drop in short order from his rifle, but he always waits for the right shot (as everyone should regardless of caliber in my opinion).
Well after all my research and questions I ended up with a Thompson Center Venture 7mm mag from Cabela's for $379 with $75 rebate. Along with I had $115 gift cards to use with my purchase so I ended up out the door for $200.
Next step I'll purchase some brass and bullets for reloading. Probably get Lapua brass and hornady and Berger bullets.