You really should start with the very first one. It's available on PSN for ~$10 or less I don't remember. The graphics might be a little choppy compared to more modern games but it is the only place you can start if you really want to appreciate this series. If you enjoy the first game then you should def. pick this collection up. I have played SH1-4 as well as Homecoming, and personally feel that after the 3rd game the whole series sort of lost its original charm...
I just got into the series a couple years ago and played Silent Hill Shattered Memories (Wii), 2, 3, and 1, in that order (I tried SH4 and thought it was crap).
After playing those, I would say to start off with SH2 to give you an accurate foray into the series. SH2 is considered by a majority of SH fans as the best in the series, and it's hailed as one of the best games on PS2. SH2 also has little to do (if anything) with the other ones regarding characters and plot, so I think that makes it a good candidate for the first game.
After SH2, I would go to SH1 if you decide to try it because it will set you up for SH3. SH1 and SH3 share some plot and character elements, so it would be beneficial to start with SH1 before SH3. If you decide not to go for SH1, then I don't think it would be a bad thing to move right to SH3 because of the graphical and technical similarities to SH2; SH2 and 3 look and play the same, as they are both on PS2. You can always just jump to Wikipedia and read up on the plot for SH1. You can look up the characters for SH1 and 3 and see the relationships between them. Although it would be best to start with SH1 storywise, you'll need a PS1 memory card to play it. As expected the graphics are pretty bad, especially if you have an HDTV; everything is very grainy. The controls aren't great, either. Don't get me wrong, it was still fun to play. It's just that with all of the modern systems and graphical/technical updates it was much more difficult to go back to PS1 than it was PS2.
I would end the series with Shattered Memories. I played it on Wii, but you can get it on PS2 as well (although I thought it was very nicely done on the Wii with the Wii remote phone sequences, controls, and graphics; look up videos of both before you make your decision). Shattered Memories is actually a reimagining of SH1. Although it has the same characters more or less, the plots are very different. Cheryl is still missing as in SH1, but Shattered Memories gets rid of the cultish/demonic plot and focuses more on the psychological component of the characters. Also, for the first time in the series you don't actually fight any monsters. You do encounter them in the Nightmare episodes throughout the game, but all you can do (and HAVE to do) is run from them. While some people hated this, I thought it was fun and scary as hell! And I thought the ending of this game was insane (although SH2's ending was awesome, too)! I couldn't put this title down once I started it.
So there you have it. The order once again...
SH2 ---> SH1 (or SH3 if you want to skip SH1) ---> SH3 (if you skipped SH1) ---> Shattered Memories (I highly recommend the Wii version)
This is hands-down one of my favorite video game series (if not my #1 favorite), and many would agree. These games are so complex psychologically, and they're psychologically troubling at times, too! They'll have you on the edge for their entirety. Enjoy, my friend. Hope this helped!