Do NOT buy a house to save on rental costs. There are many costs hidden with house ownership.
Aim to live in the house for 5 years from the closing date to break even on your expenses. So if you have plans to expand your family, get a pet or rent out a part of the home, account for it during planning.
A home search can vary from weeks to over a year, depending on your luck. Be mentally prepared for either extreme.
If interest rates are high, be prepared to afford payments for at least 3 years before there is a chance to refinance in a better market.