It’s best to wear tennis shoes when you play tennis. Duh! What I mean is: don’t wear running shoes, or basketball shoes, or even cross-training shoes.
Running shoes are great for running. They’re very light and constructed only moving straight ahead. They’re lousy for tennis. They won’t support you laterally when you twist and turn and change directions quickly.
Basketball shoes offer lots of support but they’re not designed for abrasive hard tennis court surfaces. I promise they’ll wear out quicker than any other shoes.
Cross trainers seem sensible but again, they are built for multiple surfaces. They are typically too soft for hard courts and will wear our prematurely. Experienced players won’t compromise.
Which brand is best? The one that fits best and that fits your budget. When you find it, but multiple pairs. Shoe companies change them so fast you probably won’t see that style again.
And wear thicker, padded socks for extra comfort. They may cost a little more but they last twice as long.
Be especially kind to your feet. They take quite a beating on hard courts.