They are all compatible. Generally speaking, 9-speed Shimano mountain bike parts are compatible with one another without. If there's an exception to that rule, I've never seen it.
One thing you might want to check is that your frame will be compatible with your top swing front derailleur. It's fairly likely that your touring frame is set up for bottom pull. If it is, you're better off getting a bottom-pull derailleur. There may be a way to make it work, but if so it's out of my realm of experience. And if you're getting new parts anyway it's just easier not to mess with it.
As for the shifters, just make sure that they're compatible with a 9-speed shimano mountain bike derailleur. You won't get good shifting out of one that's designed for road derailleurs.
As far as opinions and/or suggestions about what brand or model to buy specifically, those are generally considered off-topic per the FAQ.