You can definitly get a small inverter cheaper, but the cheap ones that are big enough to run a 120v 9 to 15amp power tool at 75-100% duty cycle will be hard on the tool... it will slowly fry the motor while the tool is working.... in time you will start to get a smell from the tool shortly before it stops working completely.
Its my opinion, to save your tools, You would be money ahead getting the honda 2000.... it will give much better performance than any sized inverter you buy, and is not dependent on a fully charged battery to keep working, but only a full fuel tank.
or another option is... if you have a way to handle it, is a harbor freight generator.. they make them up to 7000 working watts and the everyday cost is about $650. The smaller ones are cheaper, but i would stay above the 2500watt models for what you are going to be using it for.
they are heavy, but will run anything you have and will last a long time. I bought a 6500watt about 6yrs ago and am impressed with its dependability, but then I am NOT running it up against its limit like so many people do when they buy a cheaper undersized unit...
the rechargable tool option is a good choice also because the batteries last a good while in these newer tools... you can carry spare batteries, and the tools can be used anywhere without dragging a cord along..
But Using a gen-set will allow you to have good lighting while doing your projects