Rice likes National Merit Finalists, if you have won that in Arkansas, if you took the PSAT that will help with Rice. Rice
is very small and tough to get admitted from out of state, they prefer and accept 50% Texans, and they offer a lot of seats to URM.
UT Austin is a stretch because they only accept 8% OOS, 90% Texas and 2% international students.
https://admissions.utexas.edu/explore/freshman-profile
Berkeley, Michigan, UCLA GaTech, Purdue , UIUC accept a lot bigger % OOS.
Ann Arbor, may be a match, depending on your GPA, but its tougher than GaTech for admissions. GaTech, you must apply by Oct 15, or will be rejected, as OOS computer science are admitted under early plan almost exclusively. Thats because so many OOS students try for merit at GaTech and you can only win merit by applying by Oct 15.
For match I would say RPI, Case Western, Maryland College Park, UIUC and Purdue. You may not need that many match schools though, pick a few, and still try for your stretch list, you have a shot at some, I believe, as long as you have a near perfect GPA in math and science. Your GPA matters a LOT for many of these schools, and if you earned one B in math, physics or chemistry, and you may be rejected from most of the schools on your list.
Both UIUC and Purdue are strong in CS, and should accept you, IF your grades match your SAT math scores.
To get into computer science graduate school, its very competitive today, for a funded PhD. If you want to pay for a masters degree, then any undergrad education will be fine, but if you want funding, go to the top school you can afford. Since its free for you, for two years, might as well try for the top choices you list.
Many students applying to your list have taken BC Calculus as 10th graders, Calculus 3 as 11th graders, and linear algebra or diff eq in 12th grade. If your school does not offer advanced math, there is nothing you can do, but be aware that concurrent enrollment in a college is the norm today for students applying to Georgia Tech, Berkeley and UCLA from out of state.