depends on what kind of ride you want lor. if leisure ride it's
usually off track horses(retired racing thoroughbreds) or those
showjumping/dressage horses. off track horses are generally
Arabian, they're not very big and tall. the latter is quite big and
tall and can be quite difficult to mount. 
ponies are used in polo but they still look pretty big if you're
new to it. chances are we won't get to ride ponies. btw, ponies and
lass is different. 