I, too, have one of these "landlord special" properties.
I predict really the only thing you're going to have much trouble with is plumbing. Everything you find will be rigged, or leaks "fixed" with gobs of silicone rather than actually replacing the fitting, shut off valves omitted to save costs, etc.
Don't go crazy buying tools just yet, but be prepared for the fact that you will, over time, wind up having to invest in quality plumbing tools probably including some specialty stuff like broken stub extractors, short-throw tubing cutters, faucet seat wrenches, etc.