First time home buyer here. We are a young 4 person family looking to buy our first home. We have 40k saved/ gift from my parents to put down on a home but our income for the time being is quite low (35,000ish) while I am home with our young kids for a few years. We have 10k in a Vanguard VTSAX, 10k in a 401k, and 3k in an HSA. So not a huge stash. We have good credit--mine is 742, husband's is something similar. We have no debt of any kind.
We live in a small college town/rural pocket of the northeast. So taxes are bad but not as bad as urban areas in the region. Even with taxes, it seems to make sense to own. To give rough numbers, a $100k house might have a ~5ktax burden, but the same house would cost 1200--1400 to rent. The houses we are considering are in the 80k to 120k range. I guess I could go on with random details, but what I am seeking is general advice about how to go about purchasing a home, if it's a good idea to purchase one, what things to look out for, what I might have missed in my calculus, etc.