In this post I want to link to most of what one might need to think about in terms of purchasing a house. This certainly won't give you everything, but hopefully will provide you a place to start in terms of researching whether you should get your own place.
First, in terms of the financial aspects of homeownership, and how it compares to (say) investing in stocks, this post provides the relevant details. It contains the characteristics of a good investment, the long-term returns of house prices in general, describes how leverage works, and provides a contrarian view compared to what you'll generally hear about homeownership.
Here you'll find some of the benefits of homeownership, a discussion of whether it's better to rent or own, and a few thoughts on the potential downsides of ownerships which could quickly leave you on a sinking ship that you have no control over.
If you want to determine whether your particular case better lends itself to owning or renting, check out this post. It'll give you objective methods to determine whether a house is a bargain. Relatedly, this talks about whether buying or renting has been the better deal over various decades for different parts of the country. It also explains why renting may be better for you if you're a good saver and why homeownership may be the better bet if you need a little push at socking it away.
In terms of the financing, this post describes the benefits of putting 20% down and this post describes why a 15 year mortgage could save you ~ $100k compared to the 30 year loan. And finally, here I describe why the mortgage interest tax deduction isn't all that great of a deal.
Good luck out there, and, if in doubt, defer consumption.