jreaganmorgan: You know what? I think I have an idea that could fix the resolution problem. How about you pipe the output rendered by Outcast to an OpenGL program that scales it to the vertical resolution of the monitor and applies some filters to make it look less pixelated? And keep vertical bars to the left and right of the screen since it is easier to get used to those than looking through a tiny opening?
You can scale the game up on current monitors through graphics card settings. The problem is that most modern monitors only go as low as 640x480, whereas Outcast runs in 512x384. So even when your graphics card scales it up, there will be black bars at the top and bottom as well as the sides, because your monitor is showing the 512x384 game in a 640x480 pane, which is centered on the monitor with additional black bars on the sides so aspect ratio is preserved. Still, the game is absolutely playable this way.
I haven't tried the high-res patch myself but I hear a lot of good things. Sounds like you could at least increase the resolution to a higher 4:3 resolution such that it fills your screen vertically and has black bars on the sides.
As for first-person mode, I hardly ever used it. I wouldn't recommend trying to use it very much, Outcast is primarily a third-person game.
Still, I highly recommend trying Outcast. I played it for the first time a few years ago and it was the best game I played that year.
EDIT: GOG did a great job addressing any technical difficulties in the game. It will run fine by default, although at that low resolution I mentioned. If you enable scaling on your graphics card, you will only have 50-pixel bars at the top and bottom of your screen (for me this was about an inch, but it will depend on the actual size of your screen), and bigger bars on the sides. I haven't tried the high-res patch though so that might be harder to deal with, if you decide you want a bigger image.