For a beginner Alto Saxophone player, what is the best brand/model? My budget is around 1000$USD?

Thank you!

Rent first. If you are beginner, rent while you figure out if this is really what you want to do. Then, once you have established that you like the instrument, and that it is what you want to stick with it, you can either keep the instrument you are renting (most stores have rent-to-own policies that are quite fair), or upgrade to a higher quality saxophone. Any saxophone you find in a good band instrument store (so in other words, not like a Music Exchange or something like that) is going to be a perfectly fine quality sax for a beginner. Don't worry about brand/model for now because it won't do anything better or worse for you if you get a great model, or a model that is just a good model.

You can buy a pretty good student horn for less than that.
I suggest that if you are really serious about playing that you buy a Yamaha (student model).
Whatever you do, don't do like me and buy a second hand alto sax on eBay. Buy new or from someone reliable you know.
It cost me a lot to exchange the eBay saxophone to an almost new one at a local store.

The Kohlert 450 Alto Sax is rated as an excellent alto sax for beginners. It lists for $1000, but you can get it for $399.99 at http://download-sheet-music-online.com/g... (just type in, Kohlert 450 Alto Sax musical instruments in the search engine on the site).

Rent first is a great idea, but if you want to actually buy one a good beginner sax is made buy the Vito Corp. or Yamaha. IF (and that's a big if) you can find a Selmer in semi-good condition for less than a Grand. GET IT.