I'm not too sure what my first ever manage sim game would have been. I think it would be... Championship manager. I remember vividly playing Championship manager 01/02 - as mentioned, this is a very dangerous game, as you will not want to stop playing it, ever!
I don't get too drawn into many games. World of Warcraft, supposedly people die playing this game? I can't play it more then about a week at a time, and now, I don't ever play it. But I can list the games I have been totally addicted to and have stole large portions of my life:
NHL 94 (still does in 2014!)
Extreme Warfare Revenge 4.2 (Wrestling Sim)
Championship Manager 01/02
Eastside Hockey Manager 2005
Eastside Hockey Manager 2007 - the single greatest manager sim ever made. I have played this game for too many hours.
Giants Killers - a soccer sim on the old Dreamcast console was really, really good!
Football Manager 2008 - the best FM game there is!
My story however isn't 'how I started playing' but it's a story nonetheless!
Out of the Park Baseball 8. I'd known about OOTP but never really bothered. I loved VR Baseball 97 on the PSX and I always had MLB games, NFL games, NHL games etc. They were shown on TV here in England so it was interesting to see a different style of sport then what we are used too. However, I always would load up OOTP 8, click around and imagine that, yes its a great game, if you can understand it! I had the Football manager UI layout burnt into my brain and I couldn't get used to OOTP. After some months I finally loaded it up and thought, no, I am going to learn this game once and for all. So I sat and read and clicked and read. I had wikipedia open to learn the baseball ratings and slowly I managed to understand who was who, and what screens did what. From there I've bought ever OOTP (just got 15 today!) and It even motivated me to go and play baseball for my local team 'Oldham North Stars'.