I am trying to mount bases on my Tikka T3. What size screws do I need?

Tikka T3 Screws

Provided that the manufacturer specifies that the bases will fit your Tikka T3, the screws should be provided with the bases.
The actual screw size is 6x48 NS and the length of the extends .142 inches from the top to the bottom of the receiver material.  You will need to add the additional thickness of your base to determine the exact length screw that you need.
Please note that the very front screw (the one closest to the muzzle of the rifle) needs to be slightly shorter than the others.  Otherwise, the screw will extend too far into the receiver and interfere with the operation of the bolt.  The best means to resolve this issue is to use a file and file off a portion of the front screw and try it in the firearm.  Continue filing off some of the material until the base fits securely on the rifle and the front screw does not interfere with the operation of the bolt.