When you live in your own apartment, you have monthly expenses in addition to rent. According to Zillow, utilities like electricity, heat, air conditioning, natural gas, cable and Internet roughly cost about 20 percent of your rent. You'll want to factor that into your overall budget, too.

There are a number of online affordability calculators that can help you during this budgeting process. For example, Zillow's Rent Affordability Calculator can help you determine your price range.

When you are getting ready to sign a lease, make sure you account for the full price of living on your own. Budgeting wisely and planning ahead can help make your first experience as a renter go more smoothly.