With Shimano STI, you will definitely need a Shimano Road Triple FD: Sora, Claris, Tiagra (I believe), 105, Ultegra. Not sure if there was a DA a triple FD. They designed those road FD’s with a shorter pull arm from pivot to cable clamp that is required for compatibility with indexing STI front shifters. The MTB FD’s (Deore, XT, XTR, not sure what the others are) have a longer pull arm that doesn’t shift correctly due to incorrect pull ratio with those road brifters.
One thing to watch out for: some of those Shimano road FD’s have a very deep inner cage plate that doesn’t seem to work on big-middle ring differences of 8T or less because it drags on the middle ring when shifted to the outer ring. Here’s the triple FD cage shape that
does work: I’d offer it for the price of postage, but this one has failed at the spring retention prong.
Don’t get me going on the value of indexing front shifts - I’m an Ergo shifter guy that can use anything in front.
BTW, a DT front shift lever can use anything also. My son’s DA 9-speed front shifter stop working, so we installed a DA front DT shifter. Works great, and more easily trimmed, for the few occasions that he makes a front shift.