Graduate Admissions - applying math phd without outside experience
REUs probably don't matter all that much. Presenting textbook chapters will not count as research experience, although depending on the material it might count as evidence that you can learn advanced material on your own. So definitely get a letter from that prof if you do a good job.

From what little you've said, you're probably only semi-competitive for a top 25 school, and probably not competitive at all for a top ten school even with stellar GREs. But there are a lot of factors in play. For example, not having taken grad-level courses is OK if you have a good undergrad math major. And outstanding letters go a long way.

As far as going to a top 25 school is concerned, people get way too obsessed with rankings. There are about fifty R1 programs in the US, and whether you go to the 20th or the 50th matters a lot less than what kind of work you do once you're there. The ranking is also not a reflection at all of the quality of the education you'll get, it only tells you in a very rough sense about the research quality of the faculty and the average talent level of the students. But the important word there is "rough."