In my opinion, a lot of this will be based on the age of your house.
If it's an older home, a LOT will be riding on your inspection. Negotiate sort of hard on the roof and plumbing issues. Sending a camera down your waste trunk lines is not part of the standard inspection item, pay more and have this done. If you end up with issues under your slab you're going to have $$$.
No matter where you are, look up the property to see if you're in a floodplain.
https://www.fema.gov/flood-mapsTry to find out if there are other issues in the neighborhood, cracked slabs, etc....
Before you move in, keep funds set aside to take care of core items before you move in.
How old is the main power panel? What's your service rating on it? If you're going to expand it, might as well do it ahead of time. When you have your electrician there, look into generator cut out, whole home surge protector and if you plan to add new outlets, ceiling fans etc... go ahead and have the electrician install everything then and there. If you're going to install more outlets in the garage, make sure they're 20A and maybe use the orange outlets so you know visually what they're for and what tools you should run off of them.
If your home has failing plumbing, look into getting replumbed. And while you're doing this, plan ahead. Maybe get it plumbed in the garage for an extra spigot. In my home we trenched and had waste water out, so I have a 3 basin SS sink which we use frequently. We also put sewer out and stubbed out H/C for future patio expansion, as well as a fresh 15A line so we can install power/lights to this future add on.
We had a fresh 15A line just for our entertainment system. Then we ran Cat5e lines all over the place (this is a 1 story), so that was pretty easy. We ran surround sound lines for everything, drops for the subwoofer etc...
We replaced all the carpet and installed wood like ceramic tiles through 75% of the house. Then patched all the holes from the plumber/electrician and re-textured and re-painted the entire house. We dropped a gas line for the kitchen range as well, double ovens are electric.
After it was all done, then over time we replaced windows, light fixtures etc... We replaced But everything in the walls was done just to make sure we could handle it all at once. It was expensive but the other option was having to deal with living there and in construction.
We also epoxied the garage floor, finished all the walls after installing 30A and 50A lines for tools, more garage lights.
So much of this depends on the individual home so your mileage will vary.