newbe question,,I need a gun.

By "single pump" do you mean a spring or gas piston air rifle? if so this is the best deal out there right now imho, the Norica Black Eagle has a nice adjustable trigger and the build quality is above all the low to mid size rifles out now.

https://www.amazon.com/gp/product/B0142BHT6A/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

Look for a .22 Cal, if you dont want to order your pellets. .25 caliber will be better for the animals you have listed. I would advise Nitro Piston, 

I say the .22 because unless you have an actual airgun store in your area it will be hard to find .25 at a Walmart or other like store. That being said a .25 would fit your needs much better. a "Springer" .22 is a little weak for coon (you will need head shots every shot) 

The Hatsan Edge or the Airtact is in your price range for both the .22 and .25 If you add an additional $50 to your budget your options open up considerably both in quality and quietness 

Just a heads up.... read up on the spring air rifles and how they shoot. there is a learning curve and it takes some target practice to become consistent with one. 

Look for one equipped with an silencer even spring air rifles are fairly loud without one. Both Benjamin and Hatsan has Spring Air in the .25 caliber in the $200 price range 

Man you might want to reconsider if coons are on your list. We have shot a lot with 177 and 22 springers. Those dudes are tougher then you think. If you find one that works consistently please post here . Because that what brought me here also, we have a few springers and I truly think you need more FPE. And why iam looking into PCPs. 

Yes do your homework. Start here 

https://www.airgunnation.com/forum/airguns/springers-pumpers-c02-vintage/

I have a Hatsan Mdl 95 in .22 cal. It is fun to shoot. But the trigger leaves a lot to be desired. And springers are “ Hold Sensitive”. Meaning you Have to hold it the same way every time or your point of impact will vary. It’s one thing when you have all the time needed to punch holes in paper. But when shooting live targets you don’t always have that time. This is when your gun needs to have a good trigger and be consistently accurate. BTW Hatsan sells factory refurbished guns a a pretty good discount. Do an online search for Hatsan USA 

Good luck with your search.

Hatsan Edge .177 .22 .25 your choice on sale for $50 at Hatsen USA. 

Picture is .25

I appreciate the info regarding Hatsan reconditioned products and their affordable price. I just purchased some older .177 rifles and pistol that are in my opinion just too nice to use. Will be sure to check out Hatsan's website. Thank you.

I check pawn shops also I have seen some decent springers/nitro piston guns for good prices. They don't always know what they have and are normally more expert in firearms

.. consider researching the .22 cal (jim shockey) benjamin steel eagle .. i got one when they first came out for around $230 - still have it, and love it .. last year during black friday / cyber monday , they were going for $150 and under (and there was 20% off coupon code for members of this site when we ordered from crosman.com) .. super quiet , american-made barrels , 20ftlbs+ , parts are easy to get and crosman has great customer service , lightweight easy to cock , comes with decent scope .. the ugly part is the trigger , but i got a $15 trigger tune kit off ebay that was super easy to install .. you'll be able to get from us here on the forum for making your new critter getter shoot better if need be .. hold out for black friday / cyber mon if you can (i prolly couldnt either) , and check into the 20% off crosman coupon code - they have wicked bad black fri / cyber mon deals direct from their site , and many other airgun retailers do ,also .. hope that helps , and welcome to airgun nation .. - paul .

SHOCKEY STEEL EAGLE

.22 cal., Nitro Piston 2, BBC, 1100 FPS, steel rifled barrel, two-stage CBT (Clean Break Trigger), Picatinny rail, integrated sound suppression, Monte Carlo synthetic stock with soft touch inserts, includes 3-9x32mm scope, 8 lbs. New 2015.