Well they didn't quite do it...they forgot to replace the stuff as it breaks

The old tool set should give you an idea of what tools you really need, and which ones have to be durable...it will also provide you with junky versions of the tools you rarely need that probably won;t break/wear out for a while since you never use them.

Buying a new complete set is just going to get you another full set, completely with the tools you never use (like a freewheel tool for a type of freewheel you don't own). If you replace (and add missing items) along the way, you will be set.