Oh man, so many fond memories
I remember playing it on my Amiga 500
Obviously also multiple times on the PC afterwards... It was called UFO: Enemy Unknown here. Can't beat free, but you can always get it cheap on gog.com too (with all the DOS Box setup included and whatnot). A true classic that's still fun to play today
The sequel X-COM: Terror from the deep was also a lot of fun and a bit more brutal than the first game. And then there's X-COM: Apocalypse... I was one of the people who really enjoyed it (but that's not something universal, like for the first game).
Highly recommended
Once you get sucked in, you'll really get into it.