Get ALL water away from your house. Slope soil for at least 6-8 feet, have gutters empty into an underground drainage system or drain each one at least 15 feet away.
Any large trees more than 40 feet or so from your house I would remove. The ones very close aren’t as much of a problem IMO. Sure they can do damage, but it won’t be catastrophic. The big ones, tall, that are 40-50 away are the ones that can produce catastrophic damage if they come down.
Whatever you think is an adequate amount of insulation in your attic, double it.
Wrap your water heater in an insulation blanket.
Install a programmable thermostat.
The last three will save you literally thousands of dollars over time.
Congrats on your purchase!!! Hope it is wonderful.
PS - reading MG’s comments about a pool reminded me of something a neighbor told me once. He said the happiest day of his life was the day he got a pool. He said the second happiest day of his life was the day he had the pooled filled in