As previously stated, blenders and food processors are
not interchangeable. They preform completely different tasks.
If you need a blender, I find that
immersion blenders work well for most tasks. They're also easier to store and much easier to clean than traditional blenders. You can get a pretty decent one for under $20.
Food processors are used for chopping and shredding, rather than blending. You can shred cheese, chop vegetables into tiny pieces, make breadcrumbs, etc. The most important thing to keep in mind is to not worry so much about the price that you buy one that's too small for your needs. My mom once bought a 1-cup food processor for $15. unfortunately, the capacity was so small it was basically useless. The only thing you could do with it was make a single serving of salsa. You should be able to find something decent for under $30.
Honestly, I think everyone who cooks needs both. I don't use either one often, but when I need them, they're indispensable. If I were you I would get the blender first, because if you need to blend something completely smooth, it's pretty much impossible to get the job done manually. You can do most of what you can do with a food processor manually (usually with a knife or a cheese grater,) it just takes a lot longer.