kingmohd84: I want a simple answer. I previously downloaded many games from GOG on great offers like Tomb Raider 1-2-3 , Abe's Odyssey, and Psychonauts . Now I own a ps3 and I do not want to re-pay for PSN games that I already paid for on GOG.
Others, especially F4LLOUT, covered the main things already. Older Windows games usually work better with DirectInput gamepads (newer like XBox360 gamepad are XInput), Logitech F310 has both DirectInput and XInput mode. With DOSBox games it probably doesn't matter as much because DOSBox translates the controls to a gamepad anyway.
Specifically for the games you mentioned (since I have tried them):
1.
Tomb Raider 1 was a DOS game, and it didn't support gamepads originally. On PC, it was specifically played with the keyboard.
But since TR1 runs in DOSBox, you can assign the keypad controls to a gamepad. I recall I was barely able to assign all, or at least the important, controls to a gamepad. But it does not support gamepads out of the box, because the original game didn't.
With later games (TR2 etc.)... I don't recall they necessarily supported gamepads out of the box either, but at least you can assign the controls to at least a DirectInput controller there.
2.
Abe's Odyssey: I'd forget about trying to play it on a gamepad. The PC version was specifically designed for keyboard play, and I think it actually plays there better than the Playstation version on PSOne. Namely, the PC version has the different communications assigned to different function keys for easy and fast access, while on the Playstation version you had to cycle through the communication options or some other more cumbersome method.
I think I tried to assign all the controls to a PC gamepad (F310), but ran out of buttons to include at least all the communication keys to it. So unless you want to play on gamepad except to reach for the keyboard whenever you want to communicate with something, I think you are better off playing it with the keyboard.
StingingVelvet: You're not going to get a more default controller than the Xbox 360 one. It might take some messing with it for some games but it's by far the most compatible out there.
With DirectInput-era Windows games (like many of those that the OP listed), it is not. With XBox360 era games, yes. Logitech F310/F510/F710 offer both.
It is indeed interesting to see whether MS keeps supporting PC gaming also with XBone controller, or is it really like F4LLOUT said, and they have just given up the PC gaming for that. Shame if they did, I hope then the Steam controller becomes de-facto standard for PC game controllers. Or even the PS4 controller.
MS keeps changing their focus and breaking things...