For me, I started in Gen 2 when I was 10, so I'm feeling pretty old XD Anyway, for me:
1: Either Red (traded for it with a friend of mine) or Yellow. Can't remember which I got first.
2: Gold, my first Pokémon game; traded for it with the same friend.
Note: I could technically be considered to have "picked" Yellow and Crystal first, since I couldn't choose what games my friend had.
3: Sapphire; made a fool of myself on release day at Wal-Mart by asking the guy to hold a copy for ten minutes while I ran to get my mom when there was an entire display case full of them XD (But that's because I'd been to several other places and they were all out, and I was a dumb 12-year-old.)
4: ...Pearl, I think, but I didn't play it much and ended up with Platinum instead.
5: SoulSilver, Black, and Black 2. Side note, SS is currently my favorite Pokémon game; Crystal was the first and possibly only game I ever bothered to complete my Pokédex in (don't remember if I ever did with Red/Yellow, but definitely nothing after), and I can't even count how many batteries I killed playing it, and SS is just more of the same awesomeness but even more awesome.
I don't have a 3DS, so no 6 :(