Pre-writing: The best way to prepare for writing compare and contrast essays is to create a pros and cons list for each of the main elements of the essay. In your case, you would create a list of pros and cons for living in an apartment and the pros and cons of living in a house. As you create lists, see if any natural categories begin to emerge. A few categories that come to my mind with this topic are: financial pros and cons, space pros and cons, and social pros and cons. Your brainstorming might lead to others along these lines.
Reference list: An essay like this is easiest when you have experience on both sides of your argument. Your own experience and observations are certainly valid if you are allowed to write this from a personal standpoint. If you do not have experience with personally living in both a house and an apartment, you might seek references first in other people who do (interviews). I also imagine there are plenty of magazine articles written on this exact subject (specifically targeted at college students and young professionals who are just starting to live on their own) so a Google Scholar search might yield results with a few topical keywords. As far as financial data goes, I encourage you to seek and compare prices of actual apartments and housing in your area. In order to make comparisons as equal as possible, choose apartments and houses in the same general neighborhoods. To make things easier, you might only focus on housing "for rent" rather than for sale, as mortgage/interest rates would only make this more complicated. Aim to compare floor plans that boast of similar square footage or equal numbers of rooms and bathrooms. This will enhance your financial comparison. Again, this information is readily available using Google or other internet search database.