Your 9speed Tiagra shifters will run happily with any 7/8/9 speed MTB mech, and 7/8/9/10 speed road mechs. A later 9speed MTB mech will give you the best clearance for bigger cassettes.
If you want to run a wide range cassette then you’re stuck with 11-34 MTB cassettes really, there are some cheap 11-36 9speed ones about but they weigh as much as a small ship (I have one in the loft you’re welcome to for cost of postage)
Front mech wise you really need to use a road one, MTB fronts don’t normally play nicely with road STIs, in some cases they can work but it’s very kit dependant. A road mech should be bodgable to work with a sensible front ratios though.
If you use a 110/74 triple crank and only use the granny and middle positions you can run something like a 30/46 or 28/44 or 26/42 at the front and will give you usable gears for on and offroad, just adjust to suit the bias and try to keep no more than 16t difference, it can worth with more but shifts can be clunky and variable.
That would be my advice if you want to use the existing STIs ^
If not then you can get much more creative, including using bar end or other shifters and use whatever the hell you want really 🙂