The first thing you’ll need to do is familiarize yourself with brands and models. There are many different brands and models of saxophones and it can be a daunting task to wade through the sea of instruments available to the prospective buyer. There’s endless amounts of information online but for many this can add to the confusion. Enlisting the help of school teachers/private lesson teachers, local professionals and music store employees will help narrow down the search. Once you’ve decided on a specific make/model or two you can then use the internet more effectively by reading reviews and gathering what you can from the manufacturer’s website to act as your own saxophone buyer’s guide.
You don't have to buy the most expensive instrument but you should always try to get the best instrument you can afford. Nicer instruments with a reputable brand name tend to hold their value much better than the smaller off-brand variety. Another factor may be the type of playing one chooses to do, you wouldn't want to bring your expensive professional model saxophone to marching band practice where it could be easily damaged. If you're just beginning your musical journey it's best to go with a good student model horn for this very reason.