re: General maintenance and improvement for my new house: what are the essential tools?

Don't go out and buy tools OP. That doesn't make sense.

Read up on how to contract out a project, and do one project at a time. What I mean by that, is that there are steps you take to build a house and you have to do some steps first. For example, you finish drywall before you paint. That's obvious.

But buy tools as you go. Some tools like a drill you don't want to go cheap, most saws are this way also. A good chop saw is well worth the money for trim work and other projects over something cheap.