Assuming I want to buy a house rather than rent, what is a good rule of thumb to determine how much I can afford given my income, savings, etc. (I am just looking to get a general number so I know when it's worth considering. i.e. I can filter Zillow by price.)

I think it depends on how much you value the house versus other things you might want in life. I would run a financial simulation with various goals and various house prices so you can see the tradeoffs of different dreams so you can make an informed decision. Anyone who gives a rule of thumb here is missing the fact that the majority of personal finance is personal. This is why I love RightCapital because you can line up various house prices and long term goals and see how the price affects the goal. For example, let's say you have a goal to retire in year X, how do various house prices impact the likelihood of your ability to do that? How many more years do I need to work to be able to retire for each 100k house I buy?

The very conservative way to do it would be for your mortgage to be 1/4 of your take home pay. If you feel like 1/3 of your income will still allow you enough wiggle room than go for it. Figure out how much you have for your down payment and how large of a mortgage you can afford

gosh i can't even fathom spending that much on my housing

Percentage of take home pay? I don't see the logic. Expenses are generally numbers, not percentage of income. If you take home 100k and spend 25k on housing, that leaves 75k for everything else. Is 75k enough? Then if you take home 200k, why can you only spend 50k? Even if expenses like tuition go up somewhat, you can still spend 75k or 100k. And if you take home 10M, why must housing be "only" 2.5M? Why can't housing cost 8M? Obviously, I think all of this is absurd, but my point is to demonstrate that "housing as a percentage of income" doesn't make much sense to me 🤷

you must be a professor of accounting or something like that