Preparing to buy first house advice

Me and my wife of 6 months are planning on buying our first house in a few months, we have around £50,000 in a savings account and our LISAs and are just waiting on my wife’s late Grandmother’s house to sell for us to inherit £50,000 of that as well, the sale of which fell through two weeks ago due to a misunderstanding with the buyers, who now remain keen. Our top end budget is £375,000 and our combined basic salary x4.5 is £280,000, we both work for the NHS and I get pay enhancements for working nights, weekends and on calls. What are the things we can do now to improve are chances of being ready to buy when we get the £50,000 (mortgage broker/advisor, life insurance etc) and does this budget seem appropriate for us?