I would also recommend a variable magnification Handgun Scope. if you are just starting hunting with your Encore you will find the lower magnification of the variable easier to use, and show the shakes less (yes they will still be there but not as noticable and therefore they will not play mind games with you).
I personally like Burris LER Handgun Scopes. I have tried a lot of scopes over the years and always go back to Burris. I think the 2x7x32mm Burris LER Handgun Scope and the 3x12x32mm AO Burris LER Handgun Scopes are two of the best scopes on the market today for Handgunners.
The 2x7x set on 2x has a very generous field of view, and the exit pupil is large enough for even a Handgun Shooting novice can find the field of view in this scope quite easily. Once the handgunner gets accustsomed to using a Handgun Scope the magnification can be increased accordingly.
As per the .243 Winchester in a Handgun, I personally think it is an excellent choice for the handgunner that wants a single cartridge / handgun for Varminting and use on Whitetail Deer. I have been hunting with a 15" .243 Winchester T/c Encore this past season. January 1st I connected on two White Tail Does with the .243 Encore. I was using a Handload with 80gr. Speer Hot Core Spitzers loaded with H-4895 to a Muzzle Velocity of 2920 FPS. This load consistantly produces 3/4" or slightly less 5 shot groups from the bench at 100 yards.
The first Doe was standing broadside at 200 yards. I placed the crosshairs mid way top to bottom, right behind the front shoulder. At the shot the Doe collapsed without taking a single step. The second Doe was about 250 yards and walking. At the shot I heard the bullet hit and the Doe just kept walking. I could see she was humped up and knew I had hit her too far back. I reloaded and fired again as soon as she stopped (she had probably covered about 40 yards I am guessing after the first shot). I held the crosshairs right behind the front shoulder, mid way top to bottom and again I heard the bullet hit, but again the Doe stayed on her feet, but not for long. After the second shot the Doe walked about 10 steps, stopped behind a tree and stood there for a moment before collapsing. She was stone dead when I got to here. All of this took longer to type it than it actually took to take place.
I also have some 95gr. Nosler Ballistic Tips loaded with H-4350 for this Encore. They shoot about like the 80's and the average muzzle for the 95's is 2707 FPS. I have not tried these on game as yet, largely due to the fact I have the Encore zeroed for the 80's.
Good luck with what ever you choose.
Larry