I've heard of - and seen - some things with the Tikka T3 and heavier recoiling chamberings that you should consider. The main issue is recoil and accuracy. There is a fellow on 24hr CF that noticed accuracy wasn't as great on the heavier recoiling chamberings (.300 Mag and up). This was cured after installing the Bell & Carlson stock. Now I didn't install the B&C stock but my .338 was generally able to do only 1.5 MOA. My friend's .300 WM had a hard time getting under MOA. The .338 WM with 250gr Partitions also had fairly heavy felt recoil - similar to a Ruger Alaskan in .375 Ruger with 300gr bullets.
For that kind of money in a .338 WM I'd look at the new Vanguard S2, which can be had for about $550. You can find a good used scope like a Leupold M8 4x or 6x for about $200 in the EE. That combo would do quite well until you save up the $ for a new scope.
And lastly, I should add that the T3 seemed very prone to rusting on the action. The barrel was ok for some reason.