A planer is used for making two edges parallel while a jointer is used for making straight or flat surfaces. Let's say you have a warped board (suppose it looks like a banana from end to end). If you pass it through a planer, it will enter as a banana and exit as a banana. A jointer, on the other hand, will shave off bits of the banana, little by little, until it comes out flat.
On the other hand, if you have a board that is one inch thick on one side, and 1/2 in thick on the other, passing it through a jointer will NOT make the two sides of the board equal. See the image below:
So, you need both. There are ways to rig a planer to flatten a board, but I don't think there's a way to make the sides of a board parallel with a jointer.
Edit With limited budgets, it's probably not a bad idea to look into a jointer/planer (e.g., https://www.grizzly.com/products/G0675). One cutter head is used for both planing and jointing--it just requires some sort of adjustment. I don't know how that adjustment is done because I don't own one. (I didn't learn about these until after I bought both a jointer and a planer).
Edit 2 Here's a video that shows you how to surface a board with a planer: http://www.finewoodworking.com/workshop/video/a-planer-sled-for-milling-lumber.aspx. I actually built this jig before I bought my jointer and found it so cumbersome that I just bought a jointer. (Although, I was using dull knives at the time, which makes it nearly impossible to pass the board through the sled without it sliding off.)
Another couple of options:
have the lumberyard surface and straightline your lumber. They do an okay job, but if you're making fine furniture, don't expect your piece to be perfectly square.
Surface your material with a handplane. This is a long process (and quite tedious), and it may cost you quite a bit to get a good hand plane capable of doing the job.