Shimano's 10-speed 105 group (5700) has a triple crank option (comes 50/39/30 and the 30T is replaceable down to 24T) and is a good mid-line choice if you can find the components at a reasonable cost and can do the work yourself. Tektro and Shimano both offer long reach caliper brakes compatible with brifters.
However, you are getting into a fairly expensive project no matter what and, unless keeping the frame is super important to you, a newer (or even new) bike with the same group could be no more expensive.