Well, 622 supports Canon's ETTL automatic flash exposure and 603 does not, so the question would entirely depend on whether you plan to use ETTL or use purely manual flash exposure, especially given the big price difference.If you get the YN 603 then make sure to get the Mark II version - they improved a couple of issues.
As mentioned above, if you're going to use eTTL then you need the 622, if you decide to stick with manual only then either the YN 603 II or the YN 560-TX. The 560-TX is a bigger unit, but allows remote control of power and zoom with the Yongnuo 560 III flashes (in case you plan to expand later). It can also trigger any YN 602 or 603 flashes (but you'd have to get an extra 603 II transceiver to work with your 568).
Okay sounds good I'm going with the 603 ii but if I buy yn 560 iii will its RF work if I have a 603 on camera and on my 568 ex iI?
Yes. You put one 603 on the camera as the transmitter, and one on the 568 as a receiver. The 560 III doesn't need a receiver, it's built in.
FYI: They just released the 560 IV. It has a built in commander like the YN 560-TX. So you can put this flash in your hotshoe and trigger any flash with a 603/602 attached as well as any 560 III or 560 IV (without receiver needed). On top of that, it can control the power level and zoom of any 560 III and 560 IV flashes, from the master unit.