Kotupod
A .300 Win Mag is a very versatile cartridge with factory ammo and even more so for handloaders. (I know you dont handload yet, and may never do so.) Would I use a .300 Win Mag on whitetail? Heck yes! Would it be my first choice? Heck no!
On the upside the combo you found is a good rifle and an excellent scope. The scope is a varmint scope and is less than ideal for deer especially if hunting in the woods where closer shots are the norm, but it will certainly work. One advantage is that you wont need a spotting scope when doing work at the bench! I usually set my scopes at 4.5x to 5.5x when hunting and when I had a 6.5-20x the minimum setting didnt bother me at all took a lot of coyotes with it, many of them with their afterburners lit.
The down side is that recoil and ammo costs may limit your shooting or your shooting pleasure. Also, the scope is a bit bigger than I like when moving through heavy brush and timber. But recoil can be managed with a PAST shoulder pad and a good recoil pad on the rifle (dont know what it comes with), and proper selection of ammo. Remington makes a 150g Managed Recoil load that should generate less recoil than a standard .30-06 load. Shooting costs can also be managed, although they will never be as low as with a .308 or .30-06 with factory ammo.
In short, the combo is nice but hardly ideal for a deer rifle unless you will be shooting across open fields. But your NEXT rifle might well be a varminter and you could always move the scope to it, replacing it on the Browning with a 3-9x. That would give you an excellent varminter rig AND an excellent rifle for anything in North America.
Take a hard look at shooting costs before making up our mind. When I was in the Air Force and gas was 25 cents a gallon, my 1967 Pontiac GTO convertible spent most of its time soaking up the Texas sun in the barracks parking lot because I couldnt afford gas. I loved it on the road, though, and if it was to do over Id still buy it. When I got my first centerfire rifle, a 7mm Mag for elk and deer, I had to start handloading so I could afford to shoot. Handloading is something you might want to consider down the road.
The rifle and scope should both last you a lifetime, even if they get separated. Cant tell you what to do, but if it wasnt too much of a stretch financially I would probably go for it. There is something to be said for quality. I was at a gun show yesterday and saw a lot of rifles and scopes that were more expensive than the combo you are looking at, many in better combinations of cartridge and scope. But given the choice between any of them and the combo you found, Id take the Browning/Leupold Vari-X III.