If you're talking about buying a horn, and want a horn that you will feel good about for a long time, then I'd first find an mouthpiece the works for you. If you have a good sax shop that has lots of horns and mouthpieces I'd rent a tenor for a month and do a deal on renting/borrowing a bunch of mouthpieces. The horn at this point isn't as important as the mouthpiece. A good playable student tenor will work fine. The tricky bit is to give each mouthpiece a lot of time as some take a long while to get used to.
Side story: I'd heard that RPC mouthpieces were really good, so purchased one without trying it (typical for me living at the end of the earth with few choices). I tried it and thought "this isn't so great" and put it aside. Some time later I decided to try it again. This time it seemed OK. So I worked with it some more. It took nearly a month for me to get what that mouthpiece had to offer with it now being my favorite alto mouthpiece. If you can do this with a tenor mouthpiece, then I think you will have the best chance of finding an instrument that will be something more than OK for the money, or just buying a name brand that doesn't suit the sound you want.
Another side story: As said, I live in a very remote area, so don't have the ability to go try saxes first. So I went ahead had purchased several "top brand" tenor saxes when I took up tenor. The first was a YTS 61 Played fine, but not much exciting about the tone (for me). So I sold that and bought a Yanagisawa 991. It had better ergonomics and an OK tone, but again just didn't do that much for me. I then switched to a Grassi pro 2000. It was a bit better, but still not it. Finally (many years later) when I was in a big city I was able to go to a good sax shop and found more of what I wanted to sound like in a Martin. This now defined what I wanted. I still play Martins and also R&C horns, which are similar, but better ergonomics. If I lived in a decent sized urban center and someone had given me the advice I'm giving you, it could have saved me fifteen years and thousands of dollars.