Man, I never thought that I would see the day when I would agree with each and every prior posting, but I do. Very good and consistent advice is being given on this question.
My opinions are:
1. If you don't hand load, then unless you already have a .308 Winchester, go with the 7mm-08. In the standard 140 grain factory load, it is one of the most perfect, pleasant and efficient deer cartridges you will ever find, for large deer or small.
2. If you don't hand load, but you already own a .308 Winchester, then don't go with the 7mm-08. The ballistics, tragectory and performance of these two rounds are extremely similar, and you willl end up with two rifles that do basically the same thing. Go instead with the 6.5 Swede, to add more versatility to your battery.
3. If you do hand load, then go with the 6.5 Swede. See the reasons given in the foregoing post. You can load up to a 158 grain bullet, or down to a light varmint round.
4. The 7 Mauser is and was a great cartridge. However, the only reason I could see to select it over the 7-08 and 6.5 is this: If you hand load, and you feel that once in a while you may want to use your rifle for much larger game than deer, such as elk, you can hand-load the 7 Mauser up to be very stout, with heavy weight bullets. (If you already own a .308 Winchester or even a 30-06 though, then this would be irrelevant. These two will handle the job with factory loads.)
Big Paulie