For homeschoolers, I suggest a team sport over an individual sport. Second, I would pick a sport that you might enjoy that requires running, strength and/or stamina. Among good choices: soccer, lacrosse, football, basketball, volleyball, water polo, ice hockey. Sports that are more individualized, but also have team elements, include swimming, wrestling, boxing, tennis, track & field.
Sports that I would stay away from as a homeschooler are any of the martial arts, golf, skating, cycling, diving, and maybe gymnastics if one of these is your only sport (ok if combined with a team sport). I'm NOT suggesting that these aren't legitimate sports or that they don't require physical stamina, technical skill, great athleticism, etc. Just that they are considered somewhat "loner" sports and there is always a concern that homeschoolers haven't had as much exposure to groups, teams, other students, etc. as their non-home schooled peers.
So, if you're going to pick a sport, pick something that will both demonstrate athleticism AND team/group participation.