So most of the advice I’ve seen so far is to do research and get recommendations from well known professors. Well, I’ll be in the honors college at a rather low-ranked (~130 US News for LACs) school. I’ve asked and in the last four years they only had one research project, over the summer, in biology, because of a grant. So I kinda doubt that I’ll have any opportunities for research at my school.
Am I screwed before I start? Could I do my own research? Would I need to do research at another school? How could I find out about these kinds of programs? Is it possible for an undergrad to do any original research in mathematics or statistics? I absolutely love the school except for this unfortunate grad school admissions hangup 
Your best bet is to apply to REU sites each year. This can provide you some of the reserach experiencethat you need. In addition to that you can see if a professor at your university is willing to work with you on a research project. Even if there are no funded research projects, there are usually possibilities to do a project. All colleges are aware that undergraduate research is an important part of the mix.
~130 is not low-ranked. You’re only thinking about it relative to other U.S. News schools, but think about it relative to the 2,500-3,000 higher education institutions in the U.S. Being in the top 150 puts you in a pretty elite group of colleges overall. About 130 means you are going to a place like Randolph-Macon, Berry, McDaniel, Morehouse, Randolph, or Whittier Colleges. I went to college across the street from Morehouse and know for a fact their professors do research on a regular basis. Poking around on the websites of McDaniel and Randolph-Macon, they have research opportunities for their undergraduates, too (R-M has a fellowship for it). Whittier College, too, spotlights undergrad research on their website.
It’s possible that you’ve come to a place where faculty simply don’t do any research, but I’d encourage you to poke around a little bit more and confirm. I’m getting the sense that you haven’t even started college yet, so give yourself and your college a chance - wait until you get on campus and start asking people in person, talking to more advanced students and professors. That’ll give you a much better sense of whether and how many research opportunities there are.
Secondly, yes, you can construct your own project. At the very least you can do independent study projects for credit. Like @xraymancs said, you can do summer REUs and other kinds of summer research experiences (like the BEST program at Columbia, if you are interested in biostatistics). [url=<a href=“https://erl.barnard.edu/research_opportunities#summerresearch%5DHere%5B/url”>https://erl.barnard.edu/research_opportunities#summerresearch]Here[/url] is a list of summer programs in the quantitative sciences for undergraduates. There are also some small grant-funding opportunities for undergraduates. If your college is located in a city or town nearby other colleges, you could do off-campus research with a professor at a nearby university.