Well, that's possible with any controller, really. You just have to use a tool like Xpadder (which apparently has gone open source - I paid 10 bucks back in the day). I got all sorts of games that never had gamepad support to work with this.

And yeah, the F310 should be a good choice, although personally I wouldn't go for a controller without vibration. Apparently you need to get the F710 if you want that. Anyway, I wholeheartedly recommend the Logitech pads. I'm still using the Rumblepad 2 (the predecessor to the F310/710) which after more than ten years still works like a charm (other than not supporting Xinput).

I don't want to be indelicate but if understood correctly the fingers that are missing should be the ones that hold the grip of the controller (pinky and ring finger) so in theory any controller should sufice, not confortable but manageable.

I don't understand the part of internet for the Steam Controller, isn't only a controller? You just need to plug in, install the drivers and play, i assume that it works outside of steam (games).

I'm sorry to hear about your injury, but I don't think you'll enjoy playing old school FPS with a gamepad very much. The ones with vertical auto-aiming still require fast reaction times, and the period between Quake and Halo would be basically hell to play with such an imprecise and clumsy instrument.

However, as far as playing gamepad-appropriate genres goes (including the modern FPS, which is d(umb)esigned to work with a controller - requires very little skill, so slow you can finish half of Doom before you get out of the tutorial, etc.), the Logitech F series is a great choice. It's well-designed, sturdy, and affordable.

Thanks very much guys.
My injury happened almost fifteen years ago, so I have adapted quite well since that time.
At that time I needed to change my interest from shooters to strategy games. Since I'm locked out of steam I can no longer play the ones I like.
I do kinda miss the adrenaline of a good FPS though.
Now that I've found GOG I'm itching to take another look.
NessAndSonic and Klumpen0815 mention an arcade type controller. This seems interesting. I wonder if this might be preferred to a gamepad?

I have a F310 and have had several. Quality overall can be hit or miss. A few failed shortly after purchase, and others have lasted over 2-3 years. I have younger kids though that may explain the faster failures of my older controllers (as the kids get older the controllers last longer). They're inexpensive and reliable. Hard to go wrong with a Logitech F310.

Arcade type controllers are typically unwieldy, unergonomic, and simply don't allow fast enough speed in usage. And depending on the model, may be limited to 8 directions. (They also lack some modern conveniences.) Also, they're quite expensive. Not quite as stupidly expensive as the XBOX Elitist controller, but up there.

I think you need to login to steam to use it. Not so great when steam fails like it did recently.

If the controllers been made a sensible shape it should fit in the palms without and need for fingers to hold it.
FPS games shouldn't be a problem with gamepads the N64 had loads of fps and that had the left stick to aim with.

If you can aim with your left hand you could try a trackball and use the keyboard with your right hand.

Huge article about the Steam Controller

I think they mention that you can add non-steam games to Steam and then use the controller for that game but it tricks the client it's a keyboard/mouse so it might not work optimal, at least not yet.

This might be relevant to this thread as well.

I'm thinking of getting one but I'm also reluctant about a controller being attached to a client even if I think the controller itself will die long before Steam does.

Thanks Paladin.
I understand the kid thing. Mine is working for her own money now, so I'm fairly safe, lol.
Cyraxpt and Spectre:
Certainly you are not insensitive. All of you are being such a great help.
Details:
Pinky and ring finger along with the thumb are all ok. Pointy is a stump and middle is shortened with the knuckle gone.
Actually, I feel very fortunate. I passed out (sleep disorder) while working on my table saw. Could have lost the hand. So you craftsmen, be careful out there.
With Steam: I tried to use their site, but was unable to. My service provider Hughes Satellite and Steam do not play nice with each other. Spent a lot of time trying to sort it out with the little help I got from both providers. Seems to be a bandwidth problem. May be, it took twenty minuets to download "Redneck Rampage" from GOG.
So in the end I can log onto steam, but I can't access anything. So I get to miss out on any Steam oriented software.
Don't think I want to mess with their controller.
Thanks for the info on the arcade controllers. Darvond.
More and more, It looks like the F310 may be the best choice. Happily the price is reasonable enough to take a chance on it.
Scartch...

Sorry to hear about your misfortune. :^(

Since you like FPS games that generally don't play well with analog sticks maybe the Novint Falcon is an option.
I should say that I myself don't have any experience with it whatsoever, it's just that I remember that this thing had a separate configuration screen in Battlefield 2.

Is something like a logitech G13 keyboard a solution for you? That's a little extra keyboard with around 20 keys that you complete can define yourself. I'm using that because I'm lefthanded and the standard programming with mouse and keyboard normally does not work well with me. I'm not sure if that's with your type of injury an option for you, but maybe you can have a look at it.

If you end up looking for a good controller where you can define which button equals which key, I can absolute recommed the Logitech F310. I'm completely satisfied with that one.

Good luck with your search!

Uhm, now that is more troublesome since it would be the bumper/trigger fingers but since we're talking about the left side and old games i don't think there should be much of a problem, i guess it would be something like this:

A - Jump
B - Crouch
X - Reload
Y - Action
Bumpers - Rotate Weapons
Right Trigger - Shoot
Analogs - Movement + Looking.

I played Quake 1 on a Sega Saturn controller so it should be fine, not sure if old pc games have controller support though...

Everything has gamepad support with QJoyPad (Linux) and Joy2Key (Windows).
You can just map keyboard or mouse commands to directions or buttons on the pad, I'm doing this all the time with old Dos games or modern games that only support XBox gamepads.
Analog looking may be the bigger problem there.

They do make USB Retro controllers like Sega Saturn ones. It registers as Direct Input if I'm not mistaken.
Clearly you haven't tried Simon the Sorcerer 3-D with them.

Well, i was thinking more of the buttons for each weapon (does all games have the rotate weapon key?) and managing inventory in games like System Shock 2.