The Dyna started in 1993 or so, before that its predecessor was the FXR, which by most accounts was a better handling and riding bike. Disclaimer: I ride an FXRS-SP. If you can find an FXR from 88 through 93, it will cost much less than a Dyna, and once you're over 2,000 RPM's hardly vibrates at all. The FXR uses a three point rubber mounting system, the Dyna is only two, which caused some problems on the early to mid 90's bikes, something about cracking the transmission?
The Dyna came with the Evo motor through 1998 or 1999, and the twinkie after that.
My personal recomendation, go with an FXR, you'll love the ride, and the Evo motor is easier to work on.
http://webpages.charter.net/bghouse/Chilly/fxrstuff.htm