If the budget is $50 I'd go with Jo's advice and get a mortar and pestle. A bit more work, but will give a nice rustic texture that's great for this kind of thing. Just mince ingredients to a fairly small size first. Some coarse salt can work as an abrasive and help the pestle dig in.
I'd be afraid that a super cheap food processor or blender would disappoint. In my early days buying kitchen stuff, I got a cheap blender at k-mart; it died the first or second time I used it (frozen cocktails). I returned it and got another one. It died just as quickly. After the fourth one broke, I gave up and got my money back. Eventually I picked up a used commercial blender at a restaurant store ... it lasted 15 years, but it cost more than $50.
