Converting from MTB style levers to STI
Shimano road and mountain shifters use a different cable pull ratio for the front derailer. It can be made to kinda sorta work, but it won't perform right. If you buy any of the currently made Shimano road triple FDs, you will run into the problem that their minimum tooth difference between the middle and large ring spec is 11 or more, whereas you need 10, and also the profile of the cage won't be ideally matched to your chainrings. The best solution is getting an IRD Alpina FD, presuming you definitely want to stay with your current crank. You may also get acceptable performance with an older 7/8s road triple FD such as FD-3303. Older ones have a min difference spec of 10.

Other than that, no issues. Note also that you can use an 8-speed STI if you want, such as Claris.