Shimano brifters won't work with a Sun Tour freewheel (I assume it is a freewheel) or cassette and the widest freewheels available in Shimano (or Shimano compatible) form are 7-speed. At minimum you will need a new freewheel, chain and shifters (assuming you can find 7-speed ones) and likely a front derailleur if you want to use brifters.

You might do better to sell the Sun Tour parts to a collector or to someone doing a period restoration and start wih all new components. Check out the C&V forum to see what interest there is in these items.