You NEED an excuse to buy tools?
I've forced myself to have an excuse to buy tools, cause I like them so much. I don't buy a tool until I need it and my bank account is much happier. That said, here is what you will need to fix a vast majoity of things on these bikes:
Set of metric wrenches and sockets
Set of JIS screwdrivers (
http://www.mcmaster.com/#jis-(japanese-industrial-standard)-screwdrivers/=2jk0oj Go about 2/3 of the way down the page, get the set of 4 standard screwdrivers for $14.05)
Feeler guages
Impact driver
Multimeter
Torque Wrench
Assorted pliers, crescent wrenches, etc.
You can probably rent a compression tester at an auto parts store like Autozone, O'Reilly's, or Napa. When I needed to change the O2 sensor in my car, I "rented" the socket that I needed for the job at Autozone. I paid for the full price of the tool, and then when I returned it, they refunded my money.
Tools are an investment, and good ones that you take care of will likely last longer than you will. Check on craigslist for used tools as well. I know there are some differing opinions about places like Harbor Freight, but I generally only get consumables (sandpaper, lubes, etc) or one-time-use tools from them. I'd rather save up and buy nice stuff than buy cheap tools.