It depends on the boot. Mine are zip ups, but when I was fitting at the tack shop I learned. Most normal ones you lace like a tennis shoe, through each whole and tie at the top. Pretty simple.
The most traditional, comfortable and durable material would be leather. There are also some rubber boots but they don't get the good fit and your legs and feet can really sweat in rubber.
Because they wont get caught on the saddle and they are just nicer to wear. It's so they won't get caught in your stirrup and they slide out easier and if you wear like joggers, since there is no...