Doesn't DosBox have a full-screen option available in its configuration file? I played with some of the old versions of DosBox a long time ago and they had such a feature, even on linux.
Regarding the original games, I still have the floppies for the first and second of the version released in the United States (old version for DOS before a patch was released), and the CD for Apocalypse. Yes, I've gotten all three to work under DosBox running on both Windows and Kubuntu Linux. Unfortunately, the copies I have aren't for sale (sorry!).
I also have to agree about Apocalypse, I personally didn't like that one too much. I also like the first better than Terror From The Deep, but that's just my personal opinion.
EDIT: I forgot to mention, the Wikipedia actually has a list of all of the X-COM/UFO re-makes, although I haven't checked that list recently and honestly don't know how complete it is. Also, if you can run Wine I suppose it *might* be possible to run one of the Windows-based ones, but I haven't tried it and can't guarantee it would work.
I also recall from somewhere someone had set up a website to play the original through an internet browser, and I tried it myself - it worked but I don't know if it's still up and don't recall the URL or where I found the link to it.