If you have absolutely no means of acquiring the first game, then I don't think it's a huge problem to directly skip to the second. I wouldn't advise it, though, I think it's one of the very very few games of its era (pre-Dreamcast 3D games, to be exact) that still work with its dated graphics and controls. Much better aged than Resident Evil 1-3, in any case.
I'd say you can start with any one game you like/can get your hands on, but do know that fans of the series generally can't agree which one's the best (or even good). SH2 certainly gets the most praise, but I don't think it's any better/more complex than 3 or vice versa. I liked the character and music of 3 a little bit better, and I think SH2 wasn't scary throughout except for the prison level, whereas 3 is my pick for scariest game ever.
The Room mixed things up a little and was really sickening and intense (especially in the second half), which I liked a lot, but unfortunately you had to play every level twice. Not as bad as it may sound, but still a minus.
I didn't beat Origins yet, it just didn't capture me when I played it, but I'll try again some day.
Homecoming I haven't played yet, either.
I appreciated Shattered Memories, but as somebody said here before, it is not a very scary game. After the second level you start to feel much safer, and it's more of a mystery story than anything else. That said, I thought it was inventive and fun to pick apart, which is no easy feat for a remake.
Downpour would be the game I'd recommend to play first, but only if you promise to play the other games, too. It's the most accessible in the series and some of the situations you get thrown in are insane. Even the introduction of sidequests worked out well in the end. That said, the main plot is a pretty bad rip-off of Silent Hill 2. Details were changed, but the gist is the same. I blame the fans for this one.