Hi!
From a non-3rd or 4th ed player/GM's point of view:
From what I've seen and read of the rules, mostly perusing these forums, and going through some supplements and the core rulebook at the local hobby store, it's my belief the SR4 rules are not very much compatible with previous editions.
Certainly, most concepts are the same, and the general premise is the same at the core.
However, to me, it feels like an entirely different game. The sci-fi elements are more present, more advanced (as would make since, given the game now takes place in the 2070's), and the Matrix is a completely different thing. However, the rules themselves appear to be solid enough that it wouldn't be very much difficult to make a game based off the 4th ed rules that takes place in previous timelines (I'm not sure I could recommend doing it the other way around: better to get a copy of SR4 and "retcon" the setting than to have to redo the characters entirely later on).
I will be getting a copy of SR4 however (order has already been placed, now waiting patiently for it to arrive) but, personally, I'll be running a different game with SR4 instead of incorporating it in my group's continuity. That's one approach, and not necessarily the one that would work best for you. Certainly, having your players go through the entire timeline is something that's bound to be very much immersive and altogether fun. Still, I stand by my recommendation that you do so using the SR4 rules if only to avoid a major character reconstruction process later on.
Have fun and good luck!