Most of what I read are nice to haves some of what I consider essentials are:
Don't know how handy you are but the basic tools are a necessity to do thing like hanging pictures, tightening a screw in a cabinet door , Changing out fixtures etc.
I would recommend programmable thermostats pretty inexpensive but can save you money in the long run. In you are high tech look into smart home ones that above adjusted via your phone. No sense hearing or cooling your house when you aren't there.
In addition to a lawn mower get garden tools like a rake, shovel, weed eater, actual snow shovel depending on climate. Come in handy to spread mulch or change out the landscaping.
Also find numbers of home repair people for those things that are beyond you ability. Get recommendations for plumbers, electricians, roof repair, etc Much better to have a list in advance instead of waiting for an emergency
Congrats on your first home!!