The 7mm-08 is one of my favorite cartridges, and the Tikka is one of my favorite rifles, and the Whitetail Hunter is my favorite model of Tikka rifles.
If you want a rifle for big game hunting (but necessarily too big, and not necessarily at really long ranges), then the 7mm-08 is it. You mentioned the Tikka blue/synthetic. Go to, if I remember correctly, gunbroker or auctionarms - there is a blue/synthetic for $399 - that is a great price.
If you want a rifle simply to punch paper, then the .223 is it. Ammo is cheap and everywhere, and recoil is, well, nonexistent. You mentioned getting a heavy barreled rifle - go to gunsamerica - I saw a Tikka Varmint in .223 for about $500 - this is also the lowest price that I have seen. (If you don't buy it - I WILL. :wink: ) I think that this would be a perfect gun to take to the range on slow weekends. Just go out there, shoot 50 to 100 rounds, and simply have fun.
Zachary