I can't answer your question about whether Aquilasax is similar to new Chinese models. Many suspect that Aquila was Chinese made, hence possibly equivalent to certain models. I have no idea which models those are.
But I can tell you that since you don't read music, transposition shouldn't be a problem. When you transpose, you look at a note on the page, and move it up or down to get the right note on your sax. Since the page is meaningless to you, it doesn't matter what the names of the notes are. You'll just play whatever you hear. If you're talking about reading chord symbols, yes you would have to transpose those. But you can get Bb or Eb fake books online for free all day long. And you won't be in any position to use chord symbols for improvisation for a few years anyway.
So get a modern tenor or alto, whichever one you prefer. Buy used if you want to save some money. Your local craigslist probably has several horns in good playing condition suitable for a beginner.
If you still want a C melody, old ones in good playing condition can still be found cheap, so you don't necessarily have to buy a junker. I have a 1925 vintage Conn C melody I got for $250 that looks like it just came out of the factory. Somebody put a lot of money into in the past only to find there was no market for it. This happens a lot.
Since you're a beginner, you don't necessarily have to get the best horn right off the bat. A Chinese horn will serve you well the next few years as you learn how to play. Then when you become fantastic, you can upgrade and will be able to get exactly what you want.
I do highly recommend you learn to read as you learn the sax. It works great with children and worked great with me. In a few months, you'll learn most of the notes and where they are on the page. Learning reading at the same time is almost effortless. I personally use beginner band books for children when I learn a new instrument from scratch. They're well paced, simple and fun. Once you have the basics down, you can go nuts on whatever advanced books strike your fancy.