Well, I have a 13x40, and it is Chinese, not Taiwanese. On some level all lathes are projects, and you test them and adjust them to make them as accurate as they need to be for what you are doing with them. Mine needed adjustment when I got it in used but new condition just to meet my initial accuracy needs. I think just about all lathes now have accuracy in their bones, but it will take some leveling, adjusting, and perhaps some scraping and shimming to get the best from them. When we buy a bargain priced lathe, we are getting a kit that needs the finishing details it did not get at the factory because they were trying to meet a price point. There are still some high quality lathes being built, and they are as good as they can make them, as delivered. Unfortunately, the amount of labor it takes to do that raises the price to where only the fussiest and well heeled can afford them. How much do you want to pay and how much work do you want to do to it to get it to your expectations? The Taiwanese _generally_ put out better quality machines than the Chinese do, at a higher price, but not nearly as good as something like a Monarch lathe, which costs a lot more. The company that was making that really nice lathe for so little money that you want to buy went out of business. TANSTAAFL. (There ain't no such thing as a free lunch...)
Sometimes the very cheapest lathes have had corners cut badly enough that they are not really salvageable to a useful condition beyond melting them down and starting over...
Edit: Let me get off my soap box and welcome you to the forum, Mal!