clemmer, don't let anyone discourage you. If you want to start at 200 yards and work your way to shooting 600 to 800 yards and have a safe place to do so, go for it. You will learn soon enough that it is not easy, but you might have fun anyway. Shutter the thought!
A few questions. Have you shot high-powered rifles much at all? How large and old are you? Recoil matters in volume shooting and though I think the .308 is a better choice for your quest, it might not be if you are slight of build or very inexperienced.
How much are you willing to pay for optics? I've not done much civilian shooting beyond 500 yds, but I know enough to know that you are going to need good glass that is built for that purpose. I typically budget to spend 66% as much on my scope as paid for the rifle. In other words, I buy a $600 rifle, it's going to get a $400 dollar scope. The exception to this rule is when I am buying a budget gun like you are. For example I paid $199 for a Savage/Stevens 200 a few years back and it bears $350 in optics. It deserves it, because as Savages will do, it's capable of incredible groups. I guess what I am telling you is, don't by a Mossberg kit gun with a $100 scope on it and expect much success shooting afar.
Also, why the infatuation with a Mossberg rifle? If you are budget conscious, as JASmith said, I would go with a Savage every day and twice on Sunday. And I own/have owned Winchesters, T/C, Ruger, Howa, S&W, Marlins, and shot many others (Mauser, Remington, Weatherby, Browning). I've had great luck with all of them, but Savage has dominated the value/accuracy market for going on 2 decades.