No, screen readers do a fine job. The most important thing you can do is follow standards like WCAG. I could give you advice, but that advice would only make things easier for people using the same OS and screen reader I do. The people who write the standards have thought about mobile, desktop, etc. They also have to think not only about fully blind people using screen readers, but also about colour blind people, deaf people, dyslexic people, low vision people using magnification, people with physical challenges, etc. Accessibility isn't just about the blind. So the best possible advice I can give you is to encourage you to learn and follow existing web standards, so your site will work for everyone.

Yeah, WCAG is where it's at. If you follow that, you're good. DOn't overuse Aria, some sites tend to do that, and it just confuses things.