Re: New Saxophone suggestion
If you're willing to consider a used saxophone you can get a world-class professional saxophone within your budget. The gold standard for classical saxophone for many years has been the Selmer Paris Super Action 80 Serie II alto. The series II is known for having excellent intonation with a great focused or centered sound. Some university professors won't even let you in their studio unless you're playing a Selmer Serie II alto. Unfortunately, brand new these horns sell for upwards of $5000.
However, you can find excellent used ones for right at or just under $3000 if you just know where to look. The key is finding one that's still pristine (well taken care of). Its also best if you can find one that's been through a professional shop and that comes with a warranty so you know its in top playing condition, in perfect regulation and has the optimal set up. If you're ready to buy now, give serious consideration to the Selmer Paris Serie II posted for sale on the Saxquest web site at the link below.
If you're not interested in used, don't fret! You can still find a great classical saxophone in your price range. Your best bet for a brand new sax that fits your budget is P. Mauriat. They make a wonderful saxophone and I know several high caliber players using the 67R model P. Mauriat for classical playing. Best of Luck!!