Well, let's give this guy a game plan to work from if he is serious about LR shooting.
Start with something you can afford to shoot. You are going to need to bust a lot of primers to learn how to dope conditions.
The least expensive and very instructional is a 22LR shot at 100 to 200yds. There are many rifles that can shoot MOA to 1.5 MOA at these distances. Very few shooters can dope enough to do that well on any given day.
You learn how to do that and you have mastered the hardest part of LR shooting.
The next 'best' choice is a fast twist 223. The Savage 10 and 12's get the nod as they come with decent triggers, are accurate and have the bits and pieces to make the trip worthwhile.
Even your AR can be made to work if fitted with the many awesome top end kits used for service rifle comps. Some shoot as well or better then a bolt rifle. Problem is most ranges don't let you shoot far.
If willing to build a rifle and want a 'true' LR cartridge, one of the easiest is the 6BR.
www.6mmbr.com for more info then you know what to do with.
By the time you wear out any of the above, you will have a solid understanding of ballistics, doping, real accuracy and how to reload (well not in the rimfire). From there, let your budget decide. Start saving for support optics. You will spend a small fortune.
I don't recommend anything larger in bore simply because of recoil and costs. I shoot alot of LR and have cannons up to the 338. Big boomers are exciting but when you burn $1 to $2 per pop, most are going to find trigger time expensive.
The 308 is an excellent tutor but it will recoil more then the 223 and ballistics are essential the same out to 1000yds.
I will not bother with the LR hunting scenerios as you are well aware of lack of experience. longrangehunting.com is an excellent location to learn more about this segment of hunting. You will be looking at very large cannons and this will be expensive.
Worry about hitting clays on the long side of 500yds. When you can pop a clay at 700 to 800yds on any given day you would hunt on, you can start thinking about hunting real game. 87gr Vmax from a 6BR is deadly at these ranges.
I have burnt alot of powder, barrels, primers, bullets, etc over the last 9yrs. Still, there are more times that the bolt is opened and another day chosen to make the shot.
LR hunting is alot of time shooting/practising and spotting game and very very few shots at them.
Jerry