Start by planning for an emergency. Smoke detectors & a fire extinguisher. Tools to turn off the water main (find that valve before you need it). Get your neighbors' phone numbers. Get the after-hour/emergency contact numbers for all your utility providers - make sure you can contact the power company when there's no power.

After that, it's largely up to you. If you're handy, you probably already have most of the tools you need. If you're not, start asking around for good repairmen. Look around for any signs of neglect that the home inspector might have missed. My gutters were clogged full of leaves for example, wasn't obvious until it rained hard.

If you have a yard, decide now if you're going to maintain it yourself or if you're going to hire a service. If you decide to do it yourself, it's fall right now, those tools are about to be on clearance.

Make a journal for your house where you record everything you've done. I like to write down the date I replace anything, and also note the make & model numbers. So, for example I know that my last hot water heater lasted 10 years, because I have that in my notes. If you are handy, having the model numbers is super-useful. For example, I've learned to keep a replacement ignitor for my furnace - it's a 15 minute job once you know to do it.