For P-Dogs, I would go with a Bushnell Engage. Watch em explode ! You can spend a lot more obviously, but on a $550 gun, a scope at $179 is all relative. That would be a fun little set-up.
X 2 on staying within a budget scaled to the rifle and your application. Easy to get into high dollar if your looking for clarity and magnification. Looks like your setting up for about 50 to 175ish shots. Obviously closer and you’ll stretch that out on Pdogs. Something in a 4-14 x XX will get you close to what you need. From there, cost will vary a lot based on tube size, objective size, glass quality, and so on