My first Dead or Alive game was DOA3, on the original Xbox. I don't know what it was, but my young self loved every bit of it. I spent hours on end beating the game with every character just to unlock the ending movie. It is also where I fell in love with Hitomi when she was actually pretty bad ass, and more of a serious character. Instead of the more kawaii version that she is today.
I did play DOA2 Ultimate, though I think I only rented it. I still had fun with it, but didn't play it as much as 3. I actually need to pick up a copy of this game for collections sake.
I then played DOA4, I spent a lot of time playing it as well, but it always just felt worse than 3 for some reason. I can't really explain why, I just wasn't feeling it very much.
Next up Dead or Alive Dimensions. Being hyped for DOA5, I bought this to hold me over, and I actually played a lot more of it than I originally thought I would. It was actually a pretty amazing game.
Somewhere after finishing DOA: Dimensions, I picked up DOA2: Hardcore on PS2, and then very shortly after that DOA1 on PS1. DOA2 was pretty fun, I wish I would have played it when I was younger. DOA1 was...just alright. It feels like more of a game to have for collector's purposes more so than anything else. Speaking of collecting, I'd like to pick up DOA1 on Sega Saturn, and DOA2 on Dreamcast.
Last but not least we go into DOA5, I played DOA5 for a good while, I enjoyed it quite a bit. So much so that I burnt myself out on it. Which caused me to skip DOA5U. I've started playing Last Round now, and I'm once again enjoying it. I'm just trying to moderate myself more so I don't feel that complete burn out. lol
I've also played the Xtreme games. Even without the ridiculous fan service, I found both of the games to actually be pretty fun, and addicting. I'd be all for DOA Xtreme 3! Make it happen! Also...I wouldn't mind a Ninja Gaiden esque DOA game. 3D hack and slash/ beat em up. That'd be pretty cool if you ask me! lol