Ditto the thoughts on the 7mm-08. A great cartridge, to be sure. That, or .308, would be my first choice. The .243 is quite capable when dealing with whitetail (or smaller animals, of course). With proper bullets and bullet placement, they are quite effective. I absolutely agree that, if the shooter is inexperienced or less than a good shot - something larger than .243 should be chosen. A larger round (with more energy, particularly at longer ranges) will give more margin for error, of course.
As for the Rem. Model 7.... a very good rifle. My first bolt-action rifle was a Model 7 LS (unlike others, I DO like the Schnabel forend). I still regret disposing of that rifle. The Model 7 action, to give a bit of background, is identical to the 700 BDL - with one significant difference. The action is designed to be compact (like the rifle), so the bolt is approx. 1" shorter than the 700 bolt. Other than the finish, that's it.
The 700 action is designed to accomodate long-action rounds, as well as short-action rounds (the difference being how long the loading/ ejection port is cut). The bolts are the same on both.
I truly loved my Model 7. It never once let me down, through quite a lot of rough-country hunting. I judged (later) that the barrel was too light for any sustained (target) shooting.... which I now do much more than hunting....but, for hunting, it is just fine. (It certainly is a nice rifle to carry all day.) My 7 always grouped less than 1 MOA... but, having a light barrel, heated up quickly and the third shot in a group tended to wander just a bit.