There are 4 types of Saxophone, soprano, alto, tenor and baritone.
The alto sax is the easiest sax to learn and is most suitable for beginners.
If you are a beginner, a student model sax is fine. This will last you for several years until you reach grade 6 or 7 standard when you should consider an upgrade to a Yamaha of professional model sax .
If you have the budget, the best instrument for a beginner is the Yamaha YAS275. This is a great sax, easy to play, holds itís value well and will probably last you forever unless you decide to become a professional saxophone player!
A new student model sax (Jupiter/Arbiter/The Horn) costs between £350-500
A Yamaha alto sax usually costs around £600
A professional model alto sax (Selmer/Yanagisawa/Keilworth/Mauriat) costs from around £1400
To get started to will also need a few reeds (Rico, strength 1.5 or 2 will be fine) and some music. If you are a beginner to the saxophone and music notation try: The New Tune a Day for saxophone. If you are a beginner to the saxophone but have an understanding of music notation try: Abracadabra for Saxophone