I'm not the biggest fan of the series, but here are some solid titles tried & true that I've played.
Rainbow Six: Lockdown (xbox)- My first entry to the series and not a bad start.
Rainbow Six: (N64) -Not sure if there's a sub title here but the one that's multiplatform. The control scheme felt excellent with the N64 controller which was a big surprise and seems there were not as many issues as the PS1/DC versions.
Rainbow Six: Vegas 1 & 2- Very deep and realistic, I haven't played a better structured online experience. Terrorist Hunt (co-op too) is superb if your not an online competitive player and story mode is above good.
Rainbox Six 3: Loved the heavy tactics involved with squad commands and was fond of the Gamecube port for some reason. The xbox version is possibly the best and polish but I still liked the GC feel much better.
This should be enough to satisfy your R6 cravings for some time.

If you can see the future while remembering the past, you may just have control of the present.