When standing, vein on top of right foot running along inside ankle and up into leg is very prominent and bulging much more noticeably that left foot.

Ok: If painful get that checked out to rule out blood clot. If not painful it may be observed, compressed with ace wrap or stockings. It could just be a varicose vein. Please see your doctor for further management.

Venous insufficiency: This is the saphenous vein. Its valves commonly become weak and cause it to become distended with blood. Blood goes to feet when standing due to gravity. This isn't harmful. If leg becomes achy, compression stockings can help.