Do you have a specific topic you want to research in Sociology? You should look for faculty who work on something similar, if not the exact same topic, and apply to those schools to work with them (maybe even contact them in advance and let them know you're interested in working with them to gauge how enthusiastic they are about taking on students). When it comes to the PhD level, the reputation of the overall school is not nearly as important as the quality of the specific program and how it fits your research interests. If you're going into academia afterwards, look into the placements of recent graduates (some departments will list them on their site, or if they're faculty somewhere, they'll have the institution they graduated from on their profile).
Universities will normally fund you to get a PhD (I work at USC and every single PhD student is funded. It's not possible to be in a PhD program without funding, even if someone is willing to pay). Since having successful PhD recipients reflects well on the university, funding packages are a way for them to attract the best candidates. It's not really a good sign if they don't offer you funding.
As someone mentioned, you have to take the GRE to get into a Sociology PhD program. It's a test with three parts: a verbal multiple choice section, a quantitative multiple choice section and a written analytic essay section. Verbal is a lot of vocab and reading comprehension. Quantitative is basic math (high school level stuff like exponents and algebra). The essay section consists of writing about a position on a topic (doesn't have to be your actual position. It just has to be well argued) and writing about the flaws of an argument they present. I found out shortly before I took the test that they make all the potential topics that might be used available online, so I would recommend practicing with those. For the PhD level, having a good analytic score is important. GRE scores are good for five years.
In your personal statement, as someone mentioned, talk about your research objectives. I would also recommend incorporating the specific faculty you want to work with to tailor it to the individual program. Admissions decisions are largely, if not entirely, made by faculty, so appeal to the faculty you want to work with.