A young, current, and one of the most popular artists, Michael Buble, has some beautiful foxtrots such as below. Michael would be my choice of artists. I suggest going into iTunes, search for Michael Buble and listen to his music.

Also, I would suggest that when you select the music, that you look for a song that fits your personalities. If you have a problem with music timing and beats, then a slow song would probably be best selected. Choose a song that fits your level of dancing.

FOXTROTS:
FOR ONCE IN MY LIFE (very slow);

COME FLY WITH ME (medium pace with nice intro);

HOW SWEET IT IS TO BE LOVED BY YOU
(while this is a swing, it is a medium paced and bouncy);

I'VE GOT YOU UNDER MY SKIN
(medium paced, bouncy)

A popular song, THE WAY YOU LOOK TONIGHT, is also a great RUMBA by Michael Buble. I believe that Sinatra does the same song in a Foxtrot.