Thompson, Sorby, and Crown are among the best. That being said, there's no need to spend $50-$120 on one turning tool unless the money is just burning a hole in your pocket. If you're just starting out you're better off spending that money on a very good sharpening setup and decent tools. If you can't sharpen them on day one, you'll quickly become frustrated. In the decent category I'd go with PSI's Benjamin's Best line ($20'ish per tool), or maybe spend a bit more on some of the less expensive offerings Craft Supplies USA.
Just about all turning tools are high speed steel. Granted, English steel will probably be better than Chinese steel. But frankly most of us aren't going to notice that much of a difference. When you get into high end tools the better steel may hold an edge a bit longer, but it is hard to justify the price difference a lot of the time. My herd of turning tools is populated with Crown Pro PM, Sorby, Benjamin's Best and a few oddballs......From really expensive to really cheap, and I use them all.
Don't buy a set. Determine which tools you need and buy those. Most sets will include a tool or two you'll get little or no use out of.