First of all, apologies if I'm in the wrong forum! If I am, please direct me to the correct one.
I'm a Sociology major at a small state school. My goal is to get my PhD in Sociology, and some of the schools I've looked at are Duke, Harvard, UPenn, UC Berkeley, Columbia, Emory, and Rutgers. I haven't taken the GRE yet (I'm only in my second year of undergrad), but my SAT score was a 1430/1600, my GPA is a 3.98 (this includes both lower division courses and a handful of upper division courses), and I'm in the Honors program at my school.
While my test scores and grades will likely be very good when I complete my Bachelor's, I'm worried that my school isn't "prestigious" enough for the grad schools I mentioned. Like I said, I go to a small, public state university that doesn't even rank of the US News National Universities list (instead, it ranks mid-tier on the Regional Universities list). While I did gain admissions into a top tier public university, I chose to go to this school because it is smaller and offered me enough financial aid to completely fund my schooling AND pay for my living expenses.
Also, while I'm an undergrad, I plan on conducting my own research outside of my research methods classes, completing a senior thesis/Honors thesis, and joining the Honors program at the American Sociological Association. Further, I already have a positive relationship with some professors, so I should have some great LORs.
So, I guess my question is, should I care about the prestige of my undergraduate school? Are there other things (besides what I've mentioned) that I should be doing as a undergrad to be a competitive candidate for grad school? Should I consider transferring to a higher-tier school?
Some additional info on my research interests (if it's relevant): I want to study gender/sexualities, power, social interactions, and social class. For my qualitative methods course, I will be researching how trans/nonbinary students navigate dorm life. For a future research project, I would like to investigate how wealthy donors of charities view the underprivileged people they serve. I can't say for sure now what my preferred methodology would be, but I think I'm leaning toward qualitative and mixed methods.
Thank you for an insights and help!