How big 

In the simplest terms, a saxophone is just a tube that air is blown through. The keys allow you to vary the length of the tube by opening and closing holes with your fingers. The bigger the tube, the lower the sound. 

A soprano sax is a fairly small tube (about 80cm long), and so produces a relatively high sound (think soprano opera singer).

As the saxophones get bigger alto -> tenor -> baritone -> bass, so does the tube. The holes are scaled up to keep everything in proportion. Fortunately the keys remain similarly spaced out across the range, so whilst your fingers are close together on a soprano, it's not an impossible reach when you pick up a baritone. 

Different manufacturers vary the exact layout of the keys. The differences  are often only small, but you need to find something that fits with you. Most modern saxphones usually have a fairly compact key layout, so you don't need huge hands to play a baritone. 

Aside from key layout, you've also got to be able to comfortably hold a sax. One reason that altos are so popular is that they are reasonably light to hold and carry around. Get yourself a baritone, and you will notice the difference (almost 3x the weight).

Most saxes are supported by a sling that goes round the player's neck, and the right thumb. The bigger the instrument, the more you need to make sure you can stand (or sit) comfortably for a period of time. Choosing a good sling for heavier instruments is to be recommended.

In summary, try playing different sized saxes and make sure you can reach the keys without strain and support the instrument. The more comfortable a saxophone feels, the more you'll want to play. 

© 2011