PhD or Masters? For PhD, finding some way to get the attention of a specific professor can help a lot at some institutions. It varies, but many do a two-tier admission system, where first they basically rubber-stamp the admission of students who a prof has said they want to supervise, and then in a second round the usual admissions committee admits a general pool of students who aren't attached to a specific advisor yet.

One way to do that is to look at research group webpages; some actively say that they're looking for PhD students in a specific area (usually because they just got a big grant).