Go with caution on the home inspector. Most are shills for the real estate agency, and know virtually nothing about old homes. Find an inspector yourself, who does know what old homes are.
Expect problems and damage. It's not the end of the world, it's just reality with old homes. From some termite damage somewhere to poor repairs elsewhere. Old roofing shingles, leaky windows, etc.
Generically:
Wiring. Expect it to be inadequate to todays usage. Really old homes had it added after the fact, with one outlet per room, ungrounded, all on one circuit. Newer homes could have that glorious aluminum wiring mess. Otherwise, look closely for poorly done "upgrades" to the wiring.
Plumbing may well have lead solder joints on the copper fresh water lines. Test is to let the water sit for day to see if it leaches in. Effective fix is to run the water for a minute before drinking and brushing the teeth. Test for flow everywhere you need it. Old lines build up crud and restrict flow. This applies to outflow as well. Make sure every toilet actually flushes, and every drain actually flows. Expect imperfection.
Lead paint. Use a cheapie tester if you wish, they're effective. Look for it mostly on window sills and the exterior. It wasn't nearly as common on primary interior paints. Expensive to remove "correctly", easily painted over as a valid band-aid.
Asbestos. Old 9" floor tiles often have it. Those really hard decorative roof tiles also often have it. Lagging on pipes is rare on residential heating, but it can exist. Leave it alone and it won't bother you. Polish those floor tiles or poof the lagging and it can. Very expensive to remove if done properly.
Windows. They'll leak heat madly. Usually single pane. Lots of maintenance work keeping the wood in them from rotting and keeping the glass from falling out. As in repainting them every year, and probably reglazing them at least in part every other year.
Insulation. May be there, may not. May well have settled leaving gaps of several feet at the top. Often "upgraded" to enhance rotting of roofs and such. Vermin to some degree are living in it.
Heating. Probably an old furnace or boiler, that works as efficiently as older units do. IE, it's not efficient. But, many times a burner upgrade is all that is needed. Boiler tube boxes haven't changed radically, and old ones do work well at getting the air or water hot.
Cooling. Probably not there. Window air conditioners will be your friend. If the wiring is old, you want as little a unit as you can put in the windows so you don't trip breakers or pop fuses.
As for home repairs, Hope Depot on the like won't have hardly anything correct for an old home. From how to patch a real plaster wall to iron drain pipes, they are lost. You have to rise above them and do due dilligence on your repairs. But, it's not insurmountable.