Since seems you got a 9 speed shifter, you are going to need a 9 speed cassette, like the Shimano HG80 SLX 9 Speed Cassette.
As for deraileurs, you can use the Shimano RD-M615, which is marketed as 10 speed, but it will work with your setup with no problem (I used an Alivio RD which is 9 speed on a 7 speed bike for a long time, it gave me very nice shifting and reduced chain slap on that bike, which I used to go to work.) What is important to match is the shifter and the cassette, they must be of the same speed.
As for RDs, you can use practically any shadow plus RD you can get your hands on as long as its medium or even long cage. Because you are on 9 speed, the medium cage is enough for you, will give you a lighter RD with better ground clearance, but a long cage one will do the job too.
The ones you cannot use are the Zee and Saint RDs, because they are short cage model, so if you are going for double or triple rings in front, they cannot take up enough chain links for the front shifts.