You can trade between red, blue, yellow, gold, silver, crystal. The thing is, whatever you trade from gold/silver/crystal has to exist in red, blue and yellow. So no new pokemon and no new moves can be traded over. Red/blue/yellow/gold/silver/crystal is NOT compatible with any of the newer versions because the game received a major revamp in between the second and third generations.
Furthermore, you can only move pokemon from ruby/sapphire/emerald to pearl/diamond/plat/HGSS via Pal Park. Meaning you'll need a DS or DSlite in order to move it. Nothing from the 4th gen games can be moved back to the third gen games. DSi cannot palpark because in order to pal park, you need a GBA slot, which doesn't exist on a DSi.