I feel that I have a weak application. Should I take a gap year before applying to grad school?
I think you are overemphasizing the importance of the GRE. Consider it as a box you need to check, rather than "the most important factors in admission". Still, you should get started on that process only because opportunities to take the test are few and far between, and if you are ill the day you intend to take the test or otherwise do poorly, you might want a second chance.

I think you still have time to get some research experience. I don't know what is available in your field of study and at your institution, but in my field I would recommend you find a lab that would possibly be interested in hiring you on in the spring after you graduate, assuming things go well in the fall. Although applications will be due before that spring semester, at least you will be demonstrating your interest in research, and hopefully you can get a decent letter of recommendation from your research advisor.

I would also suggest finding a faculty mentor: not an administrative academic advisor, yes, those people are mostly interested in your undergraduate progress, you need to talk to professors who have gone through the grad school experience, who are involved in admissions for graduate school, etc (of course one of the disadvantages of a smaller state school is that no one there may have experience with graduate admissions, except as a student).

I don't think there is an either/or question here. If you are set on doing graduate school, you should apply and plan for what you might do to make your application better next year if you don't get into a program you like this time.