I'll add my 2 cents. Tikkas have a very good reputation for being accurate. As I mentioned in another thread, I bought a SAKO 85 Finnlight in 300 WSM that is a 2-3 MOA shooter and the SAKOs also have good reputations. After spending much time trying to make it shoot, including sending it back to Beretta twice, I discovered the the M85's have what I would call a very inadequate recoil lug system. It consists of an "L" shaped peice of aluminum the fits snugly in the synthetic stock and then a small boss in the bottom of the reciever that fits loosly into to a recess milled in the aluminum part of the lug. Sort of a 2 piece lug system. The rear action screw comes through the aluminum piece and is screw into the boss.
I love SAKO actions, especially the M85 but I will never get another one because of this lug design.
Here are some pics in this thread...
http://www.longrangehunting.com/forums/f19/no-recoil-lug-what-say-ye-49659/index3.html
You will notice that there is a cross channel machined into the bottom of the reciever. It serves absolutely no purpose. I have heard that in some previous models the lug was fitted into this channel which would make sense, but not in the M85.
I had my smith mill a lug identical to the factory lug except it had a lug milled to also fit that channel on the bottom of the receiver. He also milled the recess for the boss to fit much more snug. Cost $220.
If the Tikka's have a similar recoil lug system, I would not recommend them as a platform.
My favorite factory actions for builds and recommendations to Clemens, in order, would be the Howa/Vanguard, M70 and Rem700. That said I will not do another build on a 700 because by the time you get it close to custom action quality, you have almost paid the same as you would for a custom action and you still have a 700. The Howa and M70 need very little modifications, basically just a standard blueprint.
I would not recommend an M77 or Browning. A thorough search on those will reveal why. That said, my smith likes the M-77's, but as an all around hunting rifle, not as a precision rifle.