The cheap tests are as accurate as expensive ones, as far as I know, but like the previous poster said, be sure to check the result within the time limit. If a test line appears after the time limit, it is a negative result.
The sensitivities of cheap tests vary from brand to brand. I've seen some cheap ones on eBay that were ultra sensitive. I personally buy mine off Amazon, however I mainly buy OPKs because those are what I go through the most. I like to buy bulk packages that come with a few HPTs.
I don't understand why some people buy disposable cups for testing. I use a little 6oz yoghurt cup. I rinse it out after every use. I often take 2-3 OPKs a day for weeks on end because my cycles are irregular. My trash would fill up awfully fast if I used a new cup every time. Besides it rather seems like a waste of money. Just my opinion though. The expensive tests you buy in drugstores, you don't necessarily need a cup to use, because they have a plastic casing around them. However, you would need to dip the cheap tests into a cup.