scrap all the above, and get a cz or anything heavy bbl, not a single shot break bbl though, in 17mach2. a 17mach 2 will shoot both mach 2 and 17 Aguila rounds, that's right, two diff rounds through 1 rifle. a 17mach 2, it's trajectory is much smaller than a 22 mag, about 1/2 as small. it is deadly out to 150 yds on p dogs. a zero'd m2 at 100 yds, only drops 5 inches at 150.
Ammo cost? 1/3 the cost of 22 mag ammo, 1/4 the cost of 17hmr ammo. Ammunitiontogo.com sells a brick for 40 bucks, and a case for 35 bucks a brick.
most m2 ammo is rated at about 2100 fps, but the Eley/Remmy ammo is hotter loaded, about 2300 fps from the muzzle, so you are way faster than a 22 mag, and getting about 300 to 400 fps slower than a 17 hmr, again, for 1/4 the cost.
I would look at a heavy bbl, marlin, savage, cz , or Ruger for this. The marlins and savages can be had for about 200 bucks, the cz will be more, but can be had with a set trigger , which you can adjust down to the ounces of pull, and the ruger will be even a bit more.
Scopes? I would want power myself; anything 18 x or above. Tasco makes a scope series called the Varmint, and you can get a 6x24x42, for about 100 bucks. I have 3 of them.
Also anything Weaver will be very good, but more money. I just personally don't think a 3x9 or 4x12, looking at a p-dog, at 100 yds, will give you a big enough site picture, but that's just me...
1 more thing, if the scope says BSA, then run away!!! trust me...