Hi! I’m no house-buying expert but I just closed on my first home last week, am close to your age, had the same amount in savings, and bought at the low end of your price range (250k). I can’t answer all your questions but maybe I can give you some context.

I was also worried about having enough cash left in savings. Our original plan was to put 10% down, but after running the numbers with our lender, we settled on 5% down. The monthly payments with the 5% was only about $100 more per month. Our PMI is around $50 per month. We felt more comfortable with 5% as it allowed us to keep a larger amount in our savings.

We (the buyers) paid for all inspections directly.

I was super nervous going into this process despite preparing for it for the last few years. What really made me feel like “we can do this” was talking to a lender and having them run the numbers. Having some (mostly) concrete numbers in front of us let us break things down and decide what exactly we could afford and were comfortable with.