Make sure you don't have shitty homeowners insurance, understand generally what it does and doesn't cover. Know the age of the roof, as well as major appliances. If you have any exterior masonry at all, check the grout and try and get maintenance on it every 3-5 years. Check the basement for water intrusion if you have one, check the attic for the same/mold. If the house is old (pre-1970s), don't demo shit unless you are certain there isn't asbestos.
You have just accepted a huge responsibility. Start putting money aside for general maintenance and emergencies - don't be one of those fucking morons that thinks homeowners insurance covers everything. You generally will be responsible for plumbing repairs (in the home and excavating in the yard), appliances breaking down, HVAC breakdown, ground water intrusion, mold (even if you have mold coverage), rot, insect/rodent/bird infestations, utility company related losses, settling and foundation issues, general wear and tear/deterioration, etc.