I don't know from personal experience but I've done a little research on the Tikka T3 rifle and it seems to be a pretty solid gun for the price.
The first rifle I purchased was a Ruger M77 Mk II in .270 caliber topped with a Leupold Vari-X II 3-9x40 scope. I paid $399 bucks for the rifle (on sales at Dicks) and recieved the scope as a Christmas present (it retailed for $220 at the time). It was an excellent rifle and I killed a couple dozen deer with it. The only complaint I had was it's trigger which I fixed with an aftermarket job. The new Ruger M77 hawkeye apparently has a much better trigger than the Mk II version.
Whatever you get, purchase a good pair of scope rings and a decent scope and I'm sure you'll be happy with whatever you buy

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Good Luck!