Writing Portfolio

I’m interested in the top journalism and English programs when I apply for college next year, but I seem to be having a little trouble finding out how best to display my writing. I have many works-in-progress as well as finished works on my personal website, but none are published yet. I’m looking to get at least one or two published this summer when I have more time to expand on them, but since that is not easy, how should I go about sending in a portfolio to schools to encompass the scope of my writing?

I know that most big schools don’t have time to look through everything/anything in a portfolio, so should I also integrate some of my research and topics I’ve written about into the personal statement or a supplemental essay? Isn’t the fact that I have produced such extensive and in-depth essays on my website in and of itself a plus (or even a hook)?

Also, how and where exactly can you attach your portfolio on your application (if that is an option)?

TL;DR I’m wondering how to most effectively showcase the wide range of topics that I’m interested in and have written about even though Admissions may not read through the works.

P.S. If you guys know of any schools (probably LAC’s) that welcome/encourage portfolios or specific departments within a larger university that gives a closer look to students’ written works, please list them down below!