I have a website and blog where I discuss an original topic for which I am considering trying to get a grant for undergrad research. I have basically fleshed out the entire theory on these websites.
My question: do I need to worry about self-plagiarism if I were to attempt to get a research grant and publish a paper on this topic?
Generally, no. Self-plagiarism normally refers to reusing material from your previous published, peer-reviewed works. Using material that has not previously been published in a book, peer-reviewed journal or conference, or similar outlet, should not be an ethical problem.
Regarding grants: a grant application would normally ask what work you have already completed on the topic. Ethically, you should include any progress that is described in your blog posts. If you've already solved the problem, and you just need to put it in a paper and submit to a journal, you probably won't get the grant. But if your existing, not published-in-journals work, is only preliminary in nature, it shouldn't stop you from getting the grant, nor from using your existing work in a paper to be published. Note that for this, it is irrelevant whether your existing work has been posted on your blog or not; either way, it's progress that you should report in your application.
(Note: some of the awkward wording above is intended to clarify matters to readers who use the word "published" to include non-peer reviewed documents posted on web sites, arXiv, etc. That is not my understanding of the common usage of the word in academic circles, but I do not want to be misunderstood; otherwise I would just say "material that has not previously been published".)
I would think that "normal" rules would apply here with regard to plagiarism. Writing about similar ideas in different mediums is perfectly fine, however the re-using of text in multiple forms might be problematic (as it would normally be in multiple journal articles on the same subject, for example).
