Perhaps you want to decide on hard or soft boot. Make sure the rentals include all of the safety gear. Purchase a good quality skate with upgradeable bearings and wheels. Too often I come across beginners using inexpensive skates with weak ankle support, poor braking technology and slow bearings. Get the most enjoyment by starting out with a fine pair of skates.
Many parents decide to buy inexpensive or toy skates.
Instead, choose a good quality skate with two liners to adjust sizes. You can then get two full sizes out of a pair of skates. Women's skates compensate for a narrower foot around the heel. Go ahead and take your time in the store. Try on skates you are considering to buy for at least 10 minutes.