Short answer:

XBOX 360 controller or XBOX ONE controller

.

Why:

1. These are officially supported by many new PC games that are designed for them (that's called the XInput API), so no configuration needed, not even remapping buttons. (Super easy).

2. Where not officially supported, it's still recognised as a windows DirectX controller, so any windows game will support it, (as long as it supports joysticks/joypads and is no older than 1995 or so). You may have to re-map buttons, or even fiddle with config files, though. (Easy enough).

3. Where there is no/broken joystick support, you can use a utility that turns control pad commands into key presses and mouse movements like xPadder. (Do-able).

4. It's a pretty well-built controller. 3rd party controllers are almost never as accurate, responsive and comfortable as the ones that ship with the major consoles.

Any controller you can buy for PC can do 2 and 3, but not necessarily 1 and 4 (Note: there are a few other controllers that also support XInput, so games recognise them just like the 360 controller). I have the pc dongle and wireless x360 controller, as well as many other controllers. The dongle - Microsoft Wireless Gaming Receiver - is very cheap (you can get an off-brand one on eBay for less than $10 delivered).

The one drawback of the 360 controller is the older ones (the vast majority of them) have an average D-pad, which sucks in older emulated games (fast 2D platformers, SNES games, Streetfighter 2, etc). I recommend (and use) a USB adapter off eBay with an old SNES controller for those (though any genuine Nintendo controller - NES, N64, GC, Wii Classic controller, etc - will have a good D-pad, and the Sony ones are OK too).

Yes you can use more than 4 wireless controllers on some games. For example Gang Beasts, Knight Squad, Miner Warfare and Screencheat support up to 8 controllers via DirectInput instead of XInput.

XInput supports a maximum of four controllers at a time. This is an Xbox limit, carried over to Windows. Although as of 2010 few PC games require more than four controllers at once, DirectInput itself has no such limitation.

(Wikipedia, DirectInput vs. XInput)

DirectInput works with any controller including Xbox controllers. The use of DirectInput or Xinput is down to the developer or engine that they are using. It is not something that you can configure in Windows.

Update: I noticed that the upcoming windows wireless adapter states that it "(s)upports up to 8 wireless controllers". I wonder if they've removed the XInput limit and whether this will be for windows 10 only or if they will eventually backport to Windows 7.