A few things:
- You don't need to buy a house outright, get a loan. The only big cost is just the downpayment (5-20% of the price)
- There are no shortage of jobs out there for you as a new grad, but there are very few good jobs (at least where I live, YMMV). It's ok to work somewhere you don't like that pays the bills for a year and then find something better once you have more experience
- Another point on housing: rent as long as you can because mobility is a blessing. You may find a fantastic job across the country, and if you have a house it will make it that much harder to leave. Imo, stability is for older people who know they're going to work for a single company the rest of their careers.
A lot of this is opinion, so take it how you will.