I took the SAT when I was applying for college, but more recently there have been trends of individuals steering towards the ACT more now. However, it really depends on your study methods and which one you feel more comfortable taking. Keep in mind that the ACT has a science section and even though both exams have an optional essay, many individuals opt to complete it. If you do opt to write the essay portion then the SAT would be a 3 hour and 50 minute exam while the ACT would be a 3 hour and 40 minute exam.
A great article I found relating to the differences between the SAT and ACT is from Princeton Review: https://www.princetonreview.com/college/sat-act. It outlines much of what you need to know and even offers practice exams.
In terms of self study, make sure to pick up prep books. I particularly like the Princeton Reviews ones and Barron, although there are many other companies that offer preparation books too. They have a comprehensive guide to the exam and review each section of the test with sample questions so you can get an idea of which sections (Math, Reading, Science, Essay) you might need improvement on. Most books will include a full exam so you can time yourself and go through the problems to see how you do. My personal recommendation would be to go through 1 or 2 chapters/sections a day and do practice questions. Keep practicing and acclimating yourself to the exam. It will really help you prepare and feel more confident for when you actually take it.
If you don't enjoy constantly reading the actual books, many online websites like Princeton review offer daily questions and practice exams. Also, it really helps for me to study in a quiet place without much distraction but if you feel comfortable, maybe studying with a friend would be helpful too so you can keep each other accountable,
Best of luck to you and hope that helps!