Smaller barrels will result in tighter, doll-like curls, while a larger barrel will create softer curls or loose waves. Think about what type of curl you'd like to achieve.
Curling irons with clamps offer heat from both directions, which can give you a longer-lasting and more pronounced curl. Curling wands are considered much easier and quicker to use with less risk of dents or heat damage.
A high heat setting will set the curls better and make them last longer but can be very damaging. Inversely, lower temps are great for fine hair but can take a long time to set curls on thicker hair.