Man, where's the dislike button around here?
Star Wars: watch episodes IV, V, and VI, in the original, pre-specialized editions. Find a VHS copy if you must.
Episodes I, II, and III, have not truly been made yet. Those forgeries people are discussing were just bad fan fic made by George Lucas, who was working without the guidance of his team from the 70s. If you do watch them, watch them only after seeing the original trilogy, as they give away major spoilers.
Star Trek: 1, 2, and maybe 3 and 6. 5 was awful, 4 was cute but not to be taken seriously. The Next Generation films are okay.
The latest films, made by JJ Abrams are horrible caricatures of Star Trek, watching them is like watching a Trek parody skit on Saturday Night Live or something. If you liked ST4 you might like them, though.