Re: Greetings from a newbie!
I started on tenor, so I can't advise you to start on alto. Both alto and tenor (I believe) are good for starting--however, tenor will often be more expensive, as it's bigger! Do not start on soprano, as it is much more difficult to produce proper intonation on the soprano.
My advice would be to start with Connsaxman_Jim's list of approved saxophones, if you can find that list... Maybe Jim will pull it up for you. You can email him.
With your price range, you may need to go with a used horn on ebay, but be careful, they don't always work. Make sure there is a return policy, just in case. DO NOT buy a new one for under $500. Those are often of questionable quality, and the experience of most on this forum says to stay away from them.