Sadly, when it comes to 3rd party controllers, it's pretty much a complete crapshoot. The two biggest issues you'll run into are horrendous deadzones on the analog sticks and what piss poor quality control.
If you very specifically want an Xbox 360 model controller - and I can understand that, because I vastly prefer it to the Xbox One changes and wish Microsoft had just stuck with the exact same design but just put the new Dpad on that model - your options are severely limited. I think your only option would be one of the PDP controllers, either the Rock Candy or Afterglow. You can usually find the Rock Candy (no LED, no vibration) model for around $15. The Afterglow, assuming you can find it in stock, will normally sell for $30. I don't believe either model is hardwired anymore (the Afterglow used to be) but they are wired in the sense that they use USB cables for power (no battery option).
I've been using a Rock Candy controller for several months now (Amazon had them on sale for $11 and change) and, thus far, haven't had any major issues with it - but, again, your mileage may vary because lax quality control will let a higher percentage of bad controllers through. The analog sticks aren't as firm as an official 360 controller (though, not as loose as, say, the Dualshock 3) and they're just hard plastic (so I'd highly recommend buying some rubberized grips for them), but there's doesn't appear to be much of a deadzone or, at worst, only a very negligible one. I think the Dpad, while identical to the 360 model, is actually slightly better. It's tighter, firmer. Of course, that also makes it a little rougher on the thumb; I wouldn't recommend any 2D platformer marathons with the thing. And it seems slightly (maybe 5%) smaller than the 360 controller. The Afterglow is nearly identical to the official 360 controller other than the more budget build quality. Either controller should meet your needs, though I'd highly recommend putting the controller through its paces when you get it. Actually, I'd recommend that for any 3rd party controller.
If you're open to using an Xbox One style controller, then...well, your options are still pretty limited for anything halfway decent. I'd stick with either PDP or PowerA. Of the budget 3rd party controllers, theirs seem to be the best, though it's an extremely low bar. They're both prone to poor quality control and you definitely feel the budget in the build, but they tend to be functional. Again, if you buy one, use it excessively. Push it to see if anything is going to fail while you still have the option to return it or exchange it. If you manage to get one with decent quality, and you don't abuse it (i.e. dropping it, throwing it in a tantrum, yanking the cord from the controller, coiling the cord around the controller, etc.) then it should last you a respectable length of time. But don't expect them to last like official controllers. My 360 controller lasted a good 7 years and survived a couple drops before it started having issues. These budget controllers...if you get two years of use then I'd say you're a winner.
Personally, if it's for playing games on PC, I would just wait for a sale and then buy an Xbox One or PS4 controller. They're regularly on sale for around $40 and you get a much better build quality for that extra $10.