Budgeting should be very similar to how you do it today. The only difference is that instead of having just rent, you have mortgage, home owner's insurance, and property taxes as fixed recurring expenses. Often people will include those in their monthly payment to their mortgage company which will keep track of the balance and pay the appropriate entity when the bill is due.
Other than that, know that eventually you'll need to do some maintenance so you should make sure you have savings allocated to that.
As for furniture, this should be thought of before you purchase. If you don't have enough furniture for the size house you purchase, then you need to be able to buy what you want with cash. That means having extra savings or getting by with what you currently have until you save enough to get more. It is extremely unsmart to plan on putting purchases on a credit card you can't pay 100% when the statement comes. You'll be in debt the rest of your life and may end up losing your house.
The other items you mentioned, like car, groceries, & utilities, should all be things you currently budget and pay for. If they aren't, then it sounds like you're not renting on your own right now. The smart thing to do would be to make sure you can handle this on your own first for a year or two before you purchase. It will also give you time to save more.