I want to build a touring bike but got confused with the set up because I want to use mtb drive train i.e: mtb rd, mt fd, 44-34-24 chain ring and 9 speed cassette but I still want to use drop bar and STI lever or down tube shifter. If anyone ever use or had experience with this kind of set up please help me with the detail.
hukapits, Mountain bike drivetrains on touring bikes are quite common. The STI integrated brake/shifter levers won't work with a mountain bike FD, the pull ratio is different. Bar end shifters or DT shifters with a non indexed (friction) FD shifter are most commonly used. Be aware that the FD can be either top or bottom shifted. If the shift cable is routed under the bottom bracket shell you'll need a bottom shift FD.
However, if you have a bottom pull FD setup, you can use an IRD Alpina-d FD, an Ultegra 6503 FD, or (not verified by me, but from credible source), Tiagra 9 speed FD. Others maintain that a 10sp Ultegra 6603 FD will work too, but I am a little skeptical. I'm not sure if it would work for me. If you are willing to shimmy the FD bracket, you might get it to work. No MTB FD's will work with STI drop bar shifters.
If you have a top pull FD setup, you can try to convert it to bottom pull, or rationalize to yourself that you want bar end shifters because of their "better reliablity" and lower cost.
Rear shouldn't be a problem, as all (recent) Shimano derailers have the same pull.
Front could be iffy with a brifter. I'm running fine with a Tiagra FD on some kind of Shimano crank (46-36-26), but some people claim they don't match. You can go to either a Campy front brifter (ratcheting, not indexed), bar-ends, or a down-tube shifter if that floats your boat.
FYI, there's quite a few touring bikes spec'ed with a mountain crank, so what you're suggesting is not uncommon.