Free WordPress Theme that works well on Mobiles?

“Really nice and professional” are subjective terms. I’d suggest pulling up the Theme Directory on your phone and just going through demos to see which you like.

Pretty much any recently released WordPress theme should be mobile-friendly.

Check out this link to sort the free themes by popularity: https://wordpress.org/themes/browse/popular/

Twenty Sixteen is the most popular free theme right now. Although it has the advantage of also being the most recent default core theme.