I've done wood stove repairs before when they devolped cracks like that and the best thing I can suggest is to put a patch over and zig zag the welds or you will have the cracks reopen, lining the inside with fire brick is really the best idea, welding some angle iron in to hold the fire brick would be a good idea, this keeps the fire box hotter without deforming or burning the steel sides of the box, a hotter fire burns cleaner and burns the fuel more completely.
If you want to keep it simple, have your chimney as it exits the back drop down instead of going up, the downward loop extends down a 2-3 feet then goes up, to get a fire started you are going to need to install a "T" with a solid baffle so the smoke can go straight out and up, this will help extract a great of heat out of the smoke while still in the fire box by only letting the coolest of the smoke exit, more modern furnaces have the chimney opening at the bottom to create the same affect.
I am also a big fan of devices like the Magic Heat
I've seen a number of these devices in place and everyone seems really happy with them as they not only help move the warm air but they pull more heat out of the smoke and they have a baffle cleaner built in to keep it cleaning and working.
If you want to heat water a single loop of stainless pipe should work as a slow preheat otherwise wrapping a coil around the chimney that then goes through the fire box should heat up faster so you can heat a tank or floor faster.