Yes, SH4 was supposed to be a new franchise. I don't know why it was moved to the SH series. There are some obvious nods to the SH mythos, but it's otherwise a very different game.
Drew, it is important to play them in order. However, SH1's plot can be easily digested by reading its Wikipedia entry OR going to GameFaqs and reading a plot summary. It's hard to find a copy nowadays, and the graphics and control scheme leave much to be desired. SH: Origins is actually a really good game, despite the tedious length of the final area. I think people were excited that the game was originally going to use an RE4-type over-the-shoulder control scheme, but that was scrapped early in development in favor of a more traditional SH control scheme (robot walking, focus on melee rather than gunplay).
Origins does not suffer for this. In fact, I think it's one of the moodier SH games, and it has important things to say about the core mythos. I think it's on the PS2 now, if you don't have a PSP. Either way, it's probably cheap.
SH3 is the highlight of the series for me. It's gore-tastic and disturbing as hell. It features one of the most freaky, "that's just wrong" endings of any video game I've ever seen. The dated control scheme kind of holds it back, but SH3 is definately the high point of the series and one of the great horror games of all time.