For break downs on the road if you can handle your own flat tires, you are about 95% covered. I'll carry a folding multi tool or something like that with me until I get a new bike sorted to my satisfaction but I've ridden for years carrying only a spare inner tube and a CO2 inflator.

For maintenance at home it depends on where you draw the line what you're comfortable doing. You'll be surprised at how much you can do with just a 5 mm allen wrench. Beyond that I recommend acquiring tools selectively as you find that you need them. And, when you decide to buy a cable cutter, step up and get a good one. Nothing is more frustrating than a brand new cable cutter that leaves one strand uncut.