Computer (to look up how to do stuff)
Cell phone (to call a pro to fix your mess, or, worse yet, 911)
With those things in place, I recommend a decent set of cordless tools. I bought a set of Milwaukee M18 tools, with a circular saw, SawZall, drill, impact driver, and yes, the stupid flashlight. I just finished building an entire house, and used the cordless tools 95% of the time. Of the set, I used the SawZall the least; all of the others were used daily. I use my shop vac every day as well. If you get into air nailers, of course you need a compressor. Building the house, I have 6 different nailers. Framing, siding, strap shot (for metal connectors), flooring, 15 ga. finish, and 18 ga. nailer. Now that I'm done, I'll sell the flooring nailer, as I have no plans at age 62 to lay another floor!
Over the years, one of my favorite tools is a saber or jig saw. You can do a lot with one. My most recent tool was one of those oscillating tools that started out as corner sanders. They are incredibly handy, performing cuts that can't be done with other tools.
Looking back, my first power tools many years ago were a drill and a saber saw. I got along with those for many years before buying everything else in the catalog. If you're a homeowner, like fixing and building stuff, have the time and the aptitude, buy GOOD tools. My corded drill (Milwaukee) saber saw (Bosch), and belt sander (Makita) were all pro-grade tools, and I've been using them without trouble since the 1970's. I don't know if today's tools are built to last 40 years, though!