Never had a chance to play this game. Thus a question: would a racing-newbie have a chance in this game? Do I need a gamepad or joystick or steering wheel of some sorts to achieve some sorts of results? Or are the controls comparably casual to, say, GTA?

It's more of a sim than GTA... but i'd imagine it'd work pretty well with a gamepad. It's built on the Mechwarrior Mercs engine, so there are a few similarities to that, but the combat is probably more like Tie-Fighter on the ground.
Back in the day I think I played it with a real joystick. (a big, heavy one with lots of buttons).
Of course, those were the days when most pc games required a joystick... these days I don't even know where mine is...
I tend to find playing with a joystick is a little more immersive as you get more feedback from the stick, whereas playing with a gamepad feels much lighter and therefore slightly less immersive... but i think it'd be fine for this game.

What if I only have keyboard and mouse? Simply no way I'm going to have any luck with this game?

From what I remember, it has too many controls for just a controller. So you'll need to use the keyboard for some things. So, in other words you might actually be better off with a keyboard/mouse setup for this game. In a way, it's kind of like Mechwarrior in cars.

I can't remember if you could even do anything with the mouse in this game other than click through menus for spare parts... but it has been many years since I played it.
I used a Thrustmaster Top Gun when I played, which worked great, but I had a few online friends that did just fine with keyboard only. Granted, they were freaks of nature.
My biggest fear right now is that the game won't support my Saitek x52 Pro. I really only need it to detect the axises as the buttons I can macro using the Saitek Profiler... but if it doesn't have analog axis control for this stick I'm probably going to pass.
I loved this game in my youth, but there's no sense in getting it if it won't work with all of my hardware*.
*I certainly don't expect it to work with my TrackIR 5.0, however.

lol. me too.
The advantage those big-old joysticks had over gamepads is that you could keep one hand on the keyboard for all the sim controls, and the other on the joystick. That's a bit more tricky with gamepads.
I think it should be reasonably playable with a keyboard (mouse not needed), but like most racing games, you'll have more fine control with an analogue control method.

XPadder is the easiest way to play retro games that only support classic joysticks. It basically just maps keyboard keys to a directx input device.

Reference cards for keyboard/joystick controls are here. There are no built in mouse controls.

Back in the day I used a joystick with a hat-switch and six buttons (Thrustmaster Top Gun Fox 2 Pro). Especially that hat-switch was a plus when aiming your handgun while turning your car at the same time.
When I76 hits gog.com, I'm going to use my XBox-360 pad or my Saitek Cyborg Evo Force (hat-switch, twelve buttons, ff). I probably stick with the joystick, so I have one hand left for the keyboard for either radar/targetting controls, weapon management or external views. I76 feels like a flight-sim anyway, so a joystick might be the best way to go.

The best player on the most competitive ladder in 1997 played keyboard only, so I expect you can manage.

I'm familiar with the software. However, doesn't it just turn analog direction axises into digital keyboard inputs? If that's all I could get out of my joystick I'd be better off playing keyboard only.

Just like MW2,3,4 , the best imho control setup for I'76 is keyboard/'sidewinder' joystick (iirc any that support a twisting stick).

In this instance you just map keyboard keys for movement to the joystick axis. This works surprisingly well. And map whatever other keyboard keys you want to the joystick buttons. I have an Xbox360 controller and tried it. It worked just as well as my old Thrustmaster did back in it's day. As a side note, this game translates well to dual-stick controllers.

Did your 360 work without the use of Xpadder? If so, great. If not, you aren't getting analog controls for controls that, in my opinion, require analog control. Like steering, for instance.
Please report back as to whether or not the use of XPadder is required for your newer gamepad, as I'm sure if the game supports the analog axis on an Xbox 360 controller, it will have no problems seeing my Saitek.