Allen wrenches, chain tool, spoke wrench and a leatherman.
This is a start.
Take the Allen wrenches that fit your bike, typically 3,4,5,6 and perhaps 8 mm if your crank bolts need it. Get good quality wrenches and be sure they are long enough to be useful. Many multi-tools have all of these sizes but are shaped so they aren't really functional.
Open end or box wrenches in 8,9 and 10 mm may be useful or completely unneeded depending on your bike.
A small chain tool and include a short length of chain plus a couple of suitable master links or Shimano's joining pins if you have a Shimano chain.
A spoke wrench to match your spoke nipples is also good.
Small screwdrivers, flat blade and Phillips, can be useful.
Small needle nose pliers.
The obvious; tire levers, spare tubes, patch kit, minipump.
Spare parts within reason like one brake and one shift cable, brake pads, etc.