i have two comments to make.
1) Linux is distributed under the GPL liscense. It doesn't prohibit the use of the code in commercial products, but it does require a) that software which makes use of GPL code is also distributed under the GPL and b) that you must release your source code to the public.
Linksys uses linux in their products, but they also have a download section where you can get the full source for their firmware. If your company isn't down with this then you might look into freeBSD. The bsd liscense pretty much lets you do anything you want with the code besides claim that you wrote it. You don't have to release your source or anything. That said, it would be quite a bit more difficult to distill freebsd to a embeddable size... whereas there are linux projects that have already done this (namely busybox)
2) I would imagine that for an embedded system, you are going to want to minimize the size of your OS as much as possible. Therefore i don't think Ubuntu or the like would be a wise choice for an embedded system. the base system alone takes up a good 350MB. Not to mention, on a 386, it would run _extremely_ slowly.
Something you may want to look into is busybox (http://www.busybox.net
). It is basically an entirely self-contained linux-based system packed into a single executable. The point of it is to run in an embedded environment where smallness and speed are important. It isn't a full distribution but it does have the basic unix tools you would need.
busybox is only a base system, however, so you would need to install everything else manually. I'm not sure what you would need for the thing that you're talking about doing, you explanation was vague. However, using busybox I doubt that you would need 1-2gb of flash, it would depend on your program.
3) Since you've never dealt with linux before, I would also suggest downloading Ubuntu and putting it on a PC to aquaint yourself with how the system basically works. Linux is a pretty complex system and if you've never used a unix before you could find yourself in over your head pretty quickly.
I'm not sure if that helped you at all but hopefully that sheds some light.
Good luck .... Brandon