Rhys!
It just looks classic\educated. I know some people will say it wrong every name gets said wrong sometime and why dumb it down for other peoples benefit? I myself once though
Rhys was pronounced like "rise" (as in sun-rise) but it only took once to cure that. Anyways for some reason I want to pronounce
Reece like "Ree-see" and
Reese just reminds my of
Reese's Pieces (which are good but not the best reference for a name). No matter what you choose, Good Luck!