Good budget game controller for PC gaming?

I'm trying to get into games that need a game controller and would like to have a gamepad/game controller. I'm having difficulty choosing a budget one.

Looking on Amazon, there's a lot of 3rd party options, but I'm afraid that my Windows 8.1 pc might reject those controllers for some games due to Windows and Xbox policy? I don't know if that's true, if it's not please let me know.

I bought a used wireless Xbox 360 controller, but didn't realize it needs a wireless receiver that's way more expensive, so I'm going to return it.

1. AmazonBasics Xbox One Wired Controller - Black - $25
   1. Won't have issues with compatibility, but the reviews say the quality is awfully bad
2. Wired Gaming Controller, EasySMX PC Game Controller - $19-20
   1. Looks like good quality, but I'm not sure if it'll work with Windows as it's 3rd party
3. Logitech Gamepad F310 - $15
   1. Cheapest and looks decent, but again, 3rd party
4. @play PS3 Controller - $5
   1. I've heard this is the cheapest and can be found in Gamestops, but I called my local Gamestops and they don't have this

Any ideas on the best options for both quality and compatibility while keeping a budget under $30?