Unfortunately, the short answer to this question is, "it depends." If you're doing only very simple things with screen-scraper (e.g., scraping a few files once in a while) it could run comfortably in 64MB of RAM with a 500MHz processor. On the other end of the spectrum, if you're running multiple lengthy scraping sessions in parallel the memory and CPU requirements could climb quite a bit. Allocating the right amount of memory to screen-scraper invariably involves some experimentation. For example, you might run your scraping sessions in as realistic a scenario as possible, then use tools such as the Windows Task Manager or top to monitor CPU and memory usage. Remember that you can adjust the amount of memory screen-scraper is allocated by opening the "Settings" dialog box (click on the wrench icon), then altering the value labeled "Maximum memory allocation in megabytes".

It might also be helpful to look over the question below on optimizing scraping sessions.