Are there different types of saxophones?
There are four members of a larger saxophone family that are the most commonly encountered. The soprano sax is smaller than the alto sax, and can be found in both straight and curved shapes. It is higher in pitch and arguably more difficult to learn, I generally do not recommend it for beginners. The alto sax is the familiar "swan shape" and is the most popular instrument for child and adult beginners. The tenor sax is lower pitched and larger and heavier than the alto, it is suitable for teenage and adult beginners. The baritone sax is larger, heavier and lower pitched than the tenor. It is also very expensive!
Should I Purchase or hire?
It is possible to hire saxophones for a monthly rental fee. This may be an option for a few months, but it makes good economic sense after that to purchase your own instrument. A quick check of the yellow pages should set you in the right direction. I have no affiliation with any hire firms or retailers but am happy to give free advice on instrument selection to prospective students.