If you play a lot of older, non-XInput stuff, I strongly recommend a pad that supports DirectInput/XInput switching. DirectInput support on purely XInput pads is limited and will often force you to use the analogue stick even though the control is digital in nature (fighting games for instance) - the d-pad in these cases is the hat switch. Also, DirectInput force feedback isn't supported on XInput pads.

I personally use the Speedlink Torid - it's a rather cheaply made pad and the build quality isn't great, but it works with everything under the sun (PS3, Xbox 360, XInput/DirectInput switching by holding down the Guide button) and I find that it has a decent d-pad and quite responsive triggers for that price range. We have five of them in the house and it's ideal being able to swap them out between systems. I broke one by dropping it on the floor (damaged the bumper button on which it landed), but the others get more or less daily use and are still good two years later.

The Logitech F310/F510/F710 is quite good, but the analogue triggers on those things aren't the best. Analogue triggers tend to wear down and bumper buttons tend to stick after a while.

The Steam Controller isn't bad, but it's useless for anything not running in Steam - you need Steam's Big Picture mode to map the controls you need, and while you can add GOG games as non-Steam, you're still bound to Steam in this regard. Either way, it's a great sofa-bound mouse replacement, although not very good for FPS or anything that requires twitch precision control.

The DualShock 4 is a good pad, although I haven't used it extensively on my PC. I connect it on occasion to play Remote Play through the PC, but I hear there are ways to use the touchpad as a mouse.

There's no button combinations I'm aware of, but you are able to calibrate using the Logitech Gaming Software.

The only problem I had with my logitech F310 is the FUKIN SHOULDER BUTTONS. So hard to press, making my fingers cramp.

I am using Xbox controller right now as I can't be arsed with those buttons anymore. But guess what, now my LEFT THUMB is getting trouble as the diagonal buttons have different positioning.

....

I use an ancient cabled Logitech Dual Action controller, and it has served me well for many many years.

The Logitech pads (F-series) are at best only okay. I don't get why so many people recommend them. The analog sticks have ridiculously big dead zones. If you want to have any amount of movement precision look elsewhere.

I would suggest wired XBOX 360 controller over Logitech F310 for wired controller. In my experience, Logitech F310 has some problems for certain games (Dark Souls 2, for example).

the d-pad on xbox 360 controller is very bad, dont buy that.

edit:
and i didnt mention the cheap quality.

The F310 is sane and low priced.

Of modern game pads I use the Logitech F310 because it has a switch on the bottom to change between XInput & DirectInput (no need to hunt for old controllers if you want to play an old game).

My favorite game pads of all time were the Saitek P220 digital controller & the P990 analog controller. I miss those, I wonder why no one no longer puts 6 action buttons on the front of the controller.

I'm using "Oklick GP-310M" gamepad. Very nice model. Good D-pad and buttons. Had the chance to compare it with "Logitech F310". IMO Logitech is worse for me.

Addition: It is identical to "GEMBIRD JPD-DUALFORCE2" gamepad so that one ought to be fine too.

Has to be the Xbox One controller. The newest ones support blue tooth as well as 5ghz wi-fi, and all models can be attached to your PC / laptop with a simple micro USB cable. For most things it works straight out of the box, and for everything else there are XPadder profiles - I've set up a particularly great Morrowind one, where you hold down the left trigger as a "shift" button to access your hotkeys and favourites, as well as quick save and quick load.

I have no idea how the OP managed to break one - I've had mine for two years, used it over eight hours a day and I haven't even had an issue with stick drift.

I recommend them mainly because they support both XInput (for newer games) and DirectInput (for older games). With pretty much all other gamepads you are stuck to either one, which may be problematic for many games.

However, even the Logitech F-series (in DirectInput mode) has the issue that older PC games expect a rectangular movement area for the analog stick(s), while these newer gamepads (F-series, XBox360 etc.) have round analog movement. This may be a problem for some older games, ie. you don't reach the analog stick maximums diagonally.

Of course one option is to buy two different gamepads, one for XInput and another for Directinput, if one feels so. That also fixes this "rectangular movement area" problem. Besides that, I personally don't like the design and ergonomics of the XBox360 gamepad, it feels like the infamous Atari Jaguar gamepad.

As I recall, that is an old issue, apparently fixed in newer models. I haven't noticed "ridiculously big dead zones" with the F310 gamepads I've bought, and the reports also seemed to suggest that it affected only some people, possibly those with some older models. E.g. there was this Youtube video where someone demonstrated with a calibration utility how his Logitech F gamepad had indeed some issue with big dead zones, but then another video as a reply to it where the same did not happen.

I've also tested my F310 with joy.cpl, and didn't see such issue with unnaturally large deadzones.

That is just bad luck. I have had four xbox 360 controller. Apparently they are of cheap quality. Could have fooled me. One of them last well over five years of constant use before succumbing to wear and tear. The second had an unfortunate accident and the third one must be at least six years old and is only just showing signs of wear. Whilst one I bought a year ago isn't doing so well. Sometimes these things happen. They're great controllers for what they are.

^This. When my father sold his PS2 to buy an XBOX back then (a terrible mistake if you ask me), I kept the second controller in hopes of connecting it with my PC, because frankly, the Dual Shock 2 was the best and most comfortable controller I've used.

Thankfully, a good friend of mine found a way to connect it via the parallel port (involved some DIY) and I've been using it that way until I found these PS2→USB adapters. Fast forward 15 years, I still have the same controller that still works flawlessly and up to this day, I haven't found a better gamepad even though I tried a lot of them.

edit: I don't use it for pre-2000 games so I'm not sure about compatibility with older games. Having said that, the only game that couldn't "see" it was Screamer 4x4, but then again, that game had a problem "seeing" most controllers anyway.