It appears that you are asking about cartridges, not calibers.
Both the .270 and 7mm-08 are great whitetail cartridges, although I think that the 7mm-08 is the ideal whitetail cartridge for shots within reasonable distances. In the Encore, you have a relatively short barrel, or at least short compared to rifle barrels. A .270 is going to loose more velocity in a shorter barrel than a 7mm-08, which thus means that the 7mm-08 will be more "efficient" in terms of velocity. Also, the 7mm-08 kicks a bit less than the .270. As such, I would recommend the 7mm-08 over the .270 in the Encore.
As for bullets, the standard bullet weight for the 7mm-08 is 140 grains. You can shoot heavier or lighter bullets, but, I would stick with the 140s. Given that you will not be shooting at high velocities, you don't need premium bullets that will hold together upon fierce impact like a trophy bonded bear claw, Barnes TSX, or Swift-A-Frame. Any plain jane bullet will hold together - just make sure that it shoots accurately in your Encore.
That said, take a look at the Sierra Gamekings and Nosler Partitions. Yes, they are premium bullets, but not too tough.
Zachary
Zachary