Well, you have sure gotten alot of good advice. A couple of points:
The Remington 700 Classic is a great rifle, but due to the classic styling of the stock, it does not have much of a raised cheekpiece. So, if you have small cheekbones, you are going to have trouble looking through a scope. Even with the lowest scope mounts, some people have to lift their head and perch their chin on the stock, which results in a bad cheekweld, poor shooting, and a punch in the face.
For pure performance, the Tikka is a great rifle. But, it doesn't have a classic look.
For a classic rifle, that will increase in value, I would strongly vote for the pre-64 Model 70 Winchester. It will take some looking, but you will be able to find one in good shape at $1,000, though the stock will probably have to be refinished. If you take your time, however, refinishing the stocks on these is easy, because they generally have beautiful walnut, far far above what is currently being used on even high priced rifles.
As Swampy will tell you, the pre-64 Model 70 is generally a 1.5 inch MOA rifle, instead of a 1 inch MOA rifle. (If you want a 1 inch rifle, buy a Rem. 700 BDL). But for me, I say, who cares? You are buying a .30-06 to shoot big game, not to shoot prarie dogs.
Finn Aagard's favorite rifle, pictured countless times in about 25 years of his Articles, was an early commercial FN 98 rifle, in .30-06, with a stepped down military barrel (since it was made by just after the war). As he wrote, the rifle would only group 2 inches at 100 yards. And yet, he killed hundreds of head of medium and big game with it over the years, particulary elk. He thought the relentless obsession by people for 1 inch groups was absolutely ridiculous. Instead of spending countless hours shooting from a bench, he felt that people should spend their time shooting from hunting positions, and scouting the fields, if they wanted to be good hunters.
A final thought, if you decide you would like a Mauser, then I would HIGHLY recommend an FN 98 Supreme Mauser, made in the 1950s. These are beautiful commercial mausers, and Frank DeHaas refers to them in his books as the highest and best commercial mausers that were ever factory made. The stocks are French walnut, and they have beautiful checkering, including a small dot pattern around the top of the grip cap. My only criticism of these is that they are somewhat heavy. I believe that without a scope they are probably around 8 pounds. As you will find, however, all mauser 98s are heavy. Its the nature of the design and materials.
Just some thoughts.
Mannyrock