If you could only do pesting on 1 animal which would you choose and why ?

Funny, no one mentioned Eurasian (collared) doves! As an evasive species, they've been highly successful. Starting with just 6 pair in Haiti, set loose by a hurricane, they are now in every state including Alaska and Hawaii. I'd venture to say, there are more of them than squirrels, tree and ground types, altogether! It is not uncommon here in the Roswell, NM area, to see a group of over 100 sitting on a high wire. And it isn't going to stop any time soon. Here in this clime, there are at least two broods per year, and sometimes three if we have an early Spring. 

Over the years, I do not know how many I have dispatched. Last year I started to count, but quit when I reached 250. I've downed over 50 so far this month, and I haven't made a dent at my local permission. They're good to eat, but dave for every meal is getting old!!
 
Eastern grey squirrels.. so much damage they do.. Pecan trees, siding on houses, nesting in attics and chewing on electrical wires.. 
they are the reason I got into air rifles ( 9 guns later) 
I absolutely love killing them.. I put up feeders with back stops so I can shoot safely and efficiently.. I killed 137 in my yard one year. I put a dent in them.. but they kept coming..never will kill them all. 
 
7 Years ago, I would have said with a few explicatives describing raccoons. I had one dig threw my roof to make its new home, after a large bill to have the roof and ceiling repaired, I found she had moved in when the ceiling fell right on my head. The next spring another @#$%^%$& raccoon decided to move into the same spot the prior one had. This time the cost was even larger, I went with a steel roof. Just let the little @#$%^^&%& try again.

Now I've moved to a different town and a much different problem, the little @#$%^&*& nutters have to go. Since I'm on the very edge of town I have to be very careful which direction I shoot in case I miss the little buggers. I have 4 very large trees in my yard and only 2 of the trees can be targeted due to the layout. These little @##$%%&^&*& know they are safe in the other two trees and when they see me the smarter ones make a mad dash across the yard and/or roof.
 
DanWho ​the way you explained your story was hilarious !!! I am starting to see why some of you guys have a healthy dislike for the raccoons. Didnt realize that they did that much damage to houses. I just thought that they damaged agriculture not property . You don't have a .177 that you could use on the raccoons ? I would think that caliber would be OK to use .My Evanix Monster pushes out 40 ft pounds of energy, that has to be plenty for a head shot on a raccoon. Anyway that was a hilarious story but I'm sure paying for it and going through it was not . 
 
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Squirrels Squirrels Squirrels 
 
At the time I only had a Diana dual caliber, I used the .22 at a whopping 15 ft distance while she was in the corner of my kitchen spitting at me. The only other guns I had at the time was 30-06 and a .350 Remington Magnum, both just a little bit too big for indoor coon sniping and since my earmuffs were out in the truck, just a little louder than would be comfortable. I'm not sure but I dont think the woodwork would have had much liking for something a little overpowered either.

The Diana is pretty much retired, I use my .25 condor now. Back then I didn't know about pcps. Dang Ted and youtube.
 
Squirrels. They are a small target and can be a challenge if you don't understand their behavior. I also feel that more people should cull them in their urban/suburban environments because they are so over-populated and do, not only physical damage to the environment, but put the entire ecosystem out of balance. 

There are 10 times the natural woodland population of squirrels in the suburbs and cities. 

Rats with bushy tails. I'll whack em' till the day I die. 
 
Lets see, I have mice / rats / rabbits that ruin vehicle and trailer / farm equipment wiring, raccoons that eat my pecan crop, coyotes and mountain lions that eat my cattle, pigs that eat my pecan crop, dig up pastures, roads and stock ponds; grackles that have destroyed 1/2 of my hardwood trees by carrying mistletoe infection to them. Euro doves that drive off other birds. Turtles that damage my aquaculture environment and fish loving birds that eat my catfish. NO I don't think one pest animal is possible in my situation as I am at WAR! ;)
Edit: forgot the numerous snakes, bobcats, badgers, armadillos and skunks.

Thurmond
 
Man Thurmond ! I was about to say ignorantly, you dont have a problem ! You have a shooting permission from heaven ! But I don't think anyone , if they were thinking would want those kind of problems. That can NOT be easy to deal with . Sounds like you could use a little help in your neck of the woods ! At least you have a target rich inviroment my friend !
 
I know somewhere out here on New Mexico there are prairie dog towns . I just haven't been able to find them . There's a guy , I can't remember his name , wait, Jim Chapman. I think that is his name . He did a video a long time ago about how to find the Prairie dog towns by using Google Earth . I just couldn't figure it out. I would definitely love to shoot some for sure . Out here in New Mexico it's just hard to find them unless you have access to a ranch or dairy .