Pellet guns are a crapshoot in that price range. They may require some TLC to start shooting accurately enough for pest control. You don't want a BB gun.
Plinking/target - look at AirVenturi Bronco designed by PyramydAir own Tom Gaylord. Well built and extremely accurate, just may not be enough oomph for hunting.
Here are some points to consider-
-. Power plant
If you are not proficient with spring powered air rifles I would suggest choosing one with a gas ram power plant. Crosman Nitro Piston is the one you'd want, Gamo's IGT produces massive recoil, although there are a couple of new Gamo rifles that mitigate that, none in your price range. Gas rams will be a bit more quiet than springers
Multi-pump pneumatics may fit the bill if you like a workout

the cheapest and the most moddable option is Crosman 2289 aka the Bugout kit. Very accurate and just powerful enough to take down small pests. Anything larger than a squirrel will prove to be challenging though
- Scope/mounts
Virtually all rifles will include a scope that will not perform in this price range, save for a just few. Rifles with a dovetail mount will require a decent scope and mounts added and the stock one thrown away
- Trigger
Most rifles in this price range have absolutely terrible triggers. CharlieDaTuna triggers will help. Newer Gamo models include a Smooth Action Trigger that is decent, look for SAT designation
- backyard friendliness is key if you live in a densely populated area. Some rifles will have a sound dampening solution (Gamo Silent for example)
- most rifles will need a teardown and a cleaning/lube job out of the box to perform. Some will require replacing parts like seals (Crosman Nitro Venom comes to mind)
- rifle/pellet combination - people spend days and hundreds of pellets to find the right one for their rifle and practice, practice and practice. No rifle is the same when it comes to ammo.
Also, Pellets will have trajectories affected by their shape and weight (ballistic coefficient). Hunting precision will require quite some knowledge amd practice on holdover distances with a particular pellet and your scope
The worst part is there is so many models out there that don't really differ that much but it takes some knowledge to tell them apart
The Sub-$300 range is well populated but is a shot in the dark as to what exactly you will get out of your rifle. Most will be a branded Chinese import.
There are also Chinese imported rifles that go through the teardown/lube process before being sold, PM me for the link, I don't have it right now. I think the the site is called
http://flyingdragonairrifles.org/
There is a great forum - GatewayToAirguns, check it out - loads of information and great friendly people