Most of my shooting has been full bore target (.308) out to 1000 yards but dabbled in benchrest too.
The 6.5-284 is a good choice between 500-1000 yards, but only if you have a rifle that can realise that potential and hot handloads to do the job. The 6.5 Super, an improved 6.5-284 is the same. But to be accurate you will be spending big dollars on the gun. I had a bit of success with the 6mm family of cartridges like the 6mmPPC and 6.5-284.
Here are a couple of shots of those types of BR rifles.
This is a 6mmPPC light Varmint BR rifle
This is a 6.5-284 in Heavy Varmint
This is what you can expect going to play in heavy gun with .30 cal family....but big $$$
If on a budget and starting out I would strongly suggest more on the .30 cal family, like the standard .308, the .300 Weatherby Magnum, the .338 Lapua or even the Roberts family of cartridges. That way you have plenty of muzzle energy with a decent grain bullet that will not lose energy, create excessive trajectory drop or be effected by winds too much. You can also pick up a BR gun for these at reasonable $.
Whatever you choose you will be doing plenty of handloading and experimenting with different bullet weights and shapes and powder types and amounts. Be sure to record all you do as temperatures and humidity can and will play a large part of your accuracy.
The sport can be extremely expensive but you should talk to a Benchrest Captain or some of the competitors as they can give you good advice from real experience....and often know what guys are selling guns that might suit your budget and get you started.
Caution though the sport is extremely addictive as 1crock said. I was lucky I had fullbore target and combat pistol already to distract me.
Here is example of how far things can go in search of perfect accuracy and tiny groups. This is Charlie Bailey in North Carolina in 2000 on the 1000 yard target line. The rifle weighs 150lbs :devious
Here is Charlie's gun cart to move his amazing 150lb beast
Whatever you do enjoy, I loved my target shooting for many years and still think about going back to it.
Cheers, D