Well if you can get it so chambered I'd highly recommend the 358 Winchester.
When designing a new rifle you have to design the cartridge first. Since you've settled on the Encore platform that means that just about any of the major case designs are useable: rebated, rimmed, rimless, semi-rimmed, etc.
Since you've pretty much already got the 30 and under caliber range covered why not consider a medium bore. While there are a lot of definitions of medium bore my personal definition is greater than 8mm such as the new 325 Winchester and less than 416 such as the 416 Remingtion.
In a medium bore one of the first topics that come up is recoil. Some of the medium bore cartridges are almost abusive in that regard.
Recoil is a function of 2 seperate components. The first is conservation of linear momentum. What this means is that the weight of the gun multiplied by the velocity of the gun is at least as much as the weight of the bullet multiplied by the velocity of the bullet. The short story being that if you want to keep the recoil down you will also want to keep the velocity of the bullet down. The second component of recoil is the jet effect of the powder gases when the pressure chamber (chamber plus barrel) is uncorked. This additional recoil is a function of the weight of the powder gases and the exit pressure. The short story here being keep the powder weight down, have a high expansion ratio, and use the fastest burning powder that will deliver the desired velocity.
Terminal performance is largely a function of the location and the volume of the permanent wound channel. As in real estate the most important factor is location, location, location. As many have noted before me keeping the recoil managable is a great aid in shot placement.
So the next question is how low can we go in velocity before trajectory begins to really suffer. For rifle bullets with a ballistic coefficient between 0.3 and 0.5 my research indicates that 2,400 fps is just about the floor before trajectory really begins to suffer. Most hunters I know, myself included can shoot about 3 inch groups at 100 yards from a field rest. Granted that some young folks with really good eyes and a match grade rifle can shoot sub-inch groups from a bench rest. But most field grade guns and pretty good shooters can't do much better than 3 inch groups from a field rest. Lets not even discuss what Joe Average can do even from the sitting position with no field rest. With a good field rest and assuming you are in the top 25% of the people you are looking at 9 inch groups at 300 yards. This is why 300 yards is so often suggested as a practical limit on range. Lets look at a fairly typical example the Hornady 154 grain 7mm bullet with a B.C. of 0.425, a 7mm Weatherby with the long freebore can barely get this bullet up to 3,200 fps. With a 200 yard zero this bullet is down 6 inches at 300 yards. If we use a 50% overlap of the 9 inch groups at 300 yards that means that a drop of 10.5 inches is almost undetectable in the field out to our 300 yard limit. From the Hornady manual a muzzle velocity of 2,500 fps gives a 10.8 inch drop at 300 yards. So 2,500 is enough to give a 50% overlap in groups at 300 yards against the same bullet at 3,200 fps. The 2,500 fps velocity can easily be done with a 7mm-08 and this bullet.
Tne next point is penetration. Many studies have been done by the Army and the experience of numerous Professional Hunters in Africa have shown that maximum penetration with everything from solids to fairly soft softpoints occurs at impact velocities between 2,400 fps and 2,150 fps. In order to maximize the range over which this velocity range is maintained what we want it the highest possible B.C. and since Ballistic Coefficient is a function of Sectional Density we also want the highest possible S.D. or very high weight per caliber.
The other component of permanent wound channel volume is diameter.. So we also want the largest bore that we can handle driving a high BC and high SD bullet at 2450 to 2550 depending on closest range, see below..
So we want peak velocity of 2,400 fps at the closest range that shots normally occur. In some cases this is down to 20 or 30 yards, in others it may be 80 or 90 yards for the closest normal shot. Depends on the Game and the Terrain.
So in your Encore I'd recommend the rimmed 356 Winchester or the rimless 358 Winchester. This is capable of driving a Barnes Triple X at 2,550 fps at a level of recoil that is way milder than I would ever guess before I worked with the 358 Winchester in the Browning BLR Lightning. This gun weiighs 6.5 pounds sans scope has an excellent recoil pad and is just plain fun to shoot. And it delivers more energy than a 30-06, pokes a much larger hole and actually kicks less. Mostly due to efficiency. 48 grains of AA2520 in the 358 delivers more energy than 60 grains in a 30-06 and due to lower charge weight and higher expansion ratio has less jet effect recoil.
This is as close to free lunch as you're ever going to get in this world.
And should you ever want to head north you can get 2,100 with the Woodleigh 310 grain bullet which is an awesome medium range thumper fo big bears. In this situation hold the range down to 250 yards or less and you can shoot clear through big bears with this.
For white-tails around home send a 180 or 200 grain at 2550 and you've got a very mild recoil deer round out to even 350 yards with a little holdover.
