What looks attractive for English grad programs?

I’m currently a sophomore majoring in both English (Lit) and Math (Stats) and minoring in Religious Studies at Arizona State in the Honors program. I want to use my English degree to enter a good English grad school, and hopefully become an English professor in the future. From what I understand, not only are professor jobs for English PhDs scarce, but if your PhD is from a pretty mediocre grad program, your chances of getting a good professor position is hurt badly. My Math degree (although I love mathematics) is simply a fallback.

My question is, what exactly do English grad programs specifically look for in applicants? I know that a solid statement of purpose, exceptional letters of rec, and a 3.5+ GPA are a given. What else do they look for though? Publications in undergrad journals? Starting your own clubs? Writing short stories? Research with a professor? Tutoring writing?

Thanks!

Note: I’m not in English.

Starting your own club definitely doesn’t matter; writing short stories wouldn’t matter unless you wanted a PhD in creative writing. Tutoring writing would be…okay: it probably wouldn’t help tremendously but would be a small point in your favor all other things being equal.

Publications in journals (undergrad or otherwise) would be good if the publications are akin to what you’d be doing as a scholar in the field - so, for example, publishing literary criticism or analysis papers. I’m not sure how closely literature scholars work with other professors; it’s not quite like the sciences, where you’d work in someone’s lab under their supervision. However, approaching a professor in your area and asking them this very question would be a very good idea. In your field an independent study project for a semester may be the best way to do this, where you work closely with a professor but are still working on an independent paper project (which may turn into your writing sample).

For PhD, bottom line is that depts will admit applicants who look likely to complete original research (fitting well with faculty specialties) and who will have the staying power to complete a successful dissertation and eventually bring some glory to the dept/school. Example: You are most interested in 20th century lit, specifically Kerouac. You find a dept. where there is a prof who specializes in the Beats. You visit, apply, and make the case that you want to do work in Beat Lit and possibly eventually research how Kerouac’s high school football coach might have had an effect on his later travels and writings. Eyebrows are raised. Depts eat this kind of stuff up. This kind of vision for provocative, creative, self-motivated work is what lit depts look for.