Would like a pellet rifle that's accurate and under $200.
Any suggestions?

Sheridan Blue Streak---I like them with peep sight.

Depends on what you are calling pests. NONE of those I am going to recommend are good for anything but lethal intervention.

I would look on Pyramid Air, Arizona Airguns, and Utah Airguns sites and see what they have in that range.

Airgun Nation web site has some information that may be of help.

Look at AEAC's youtube videos, he has had several that he liked that fit that category

I think Benjamin Maximus (or replacement model)
will get you in the PCP game for that and like it or not, the chinese air pumps seem to work fine for low bucks.

Exercise and shooting in one package.

My Benjamin used to take 75 pump strokes for every 20-40 shots( I forget the number)