Unintentionally, I recently played through the first 4 games in the series, and realized the best order to play them through.

I started with the first Silent Hill of course, playing the PS Store version on the PS3. After finishing it, I immediately felt like continuing the story. So I went to the attic to grab my old PS2, and played through SH3. During my playthrough, walking around South Vale and especially Brookhaven and Heaven's Night made me think "It's pretty cool that you visit these exact places in SH2...." So after SH3 was done, I started playing SH2. During the playthrough, there are numerous times when you stumble across the name "Walter Sullivan" and walking through the forests and waters of SH3 immediately made me think of SH4. So long story short, after the completion of SH2 I started playing SH4 right away - and the fact that James own father Frank is in the game is fun.

I don't know if anyone's realized this before, but if you play through the first 4 games in this order, it actually makes A LOT of sense:

SH1 > SH3 > SH2 > SH4

For some reason, it feels like you're traversing through the town's history over the course of this order. It simply feels like the natural progression, especially since SH1 is more connected to SH3, and SH2 is more connected to SH4.

Yeah, this has definitely been brought up before, and I've considered playing them this way, but I don't think I have. I tend to stick to release order when I do my series playthroughs, with the exception of playing SHO first.
But, yes, the order you've mentioned definitely makes a lot of sense. I should probably actually do it this way sometime.

Well, Origins is a prequel, so maybe you could just do them like, 0, 1, 2, 3, then 4 (and ignore the others if you want). Shattered Memories is a remake (well, kind of) and therefore, it does not count as part of the main series.

If I play Origins before 1, it destroys my whole sense of logic.

I've never been a fan of Shattered Memories. That's a remake done wrong. Well, okay. It gets classed as something else, as opposed to a remake, but I just didn't like that game. Homecoming has a decent story and fine enough graphics, but everything else about it sucks. Especially the 'combat system' (which is dreadful).

Downpour is so-so. It's not the worst game ever made, but it's not splendid either. I'm sad that they messed up the HD collection, and of course - we didn't get Silent Hills, but maybe one day we will get something like another The Evil Within game to compensate us via an unrelated company.