Since I live in North America (Canada) then I'll have to list only a few of the ones I know of here. There's far more than one alloy of HSS. Some of them are exotic enough that they become much tougher to sharpen properly using standard home grinding equipment. I've tried some really cheap off the shelf HSS, I'd almost swear that key stock would have retained the edge far longer. Others were..............ok. I then decided to order some Chicago Latrobe M-2. That's when I finally clued in, There was no comparision. C/L is the only brand I have hands on experience with, But there's many more good manufacter's around. For Braised carbide tips or even solid carbide rounds and squares, I'd have to say Micro-100 is probably about the best that I know of. But proper resharpening for high quality surface finishes would require at least a diamond hone and or wheel. I think it was T.D. Walshaw who said, "It's impossible to get a better surface finish on your parts than your tools surface finish has been sharpened to." Or at least something very close to that. That always made complete sense to me.
Tool holders and replaceable carbide tips, There's far more members much better qualified than I am. I barely know enough to make somewhat semi educated guess's. Once you've figured out exactly what your looking for, From what I've found. It's getting tool holders that are short enough in heighth for your average home type lathe. There's far more selection if you can handle 1"X1" tool holders.
But there is some made with smaller dimensions. Valenite,Iscar, Kenametal would be a few names. I'd use their carbide tips too. Where it gets complicated is trying to figure out exactly what combination of tool holder and tip you need. Let's say for example you turn a lot of 6061, 7075 aluminum. They make specific types of carbide tips for doing just that. So now you need to figure out just what tool holder will fit those inserts radius, type, etc. AND is it avalible in the tool holder size you need. Your also dealing with positive/negitive rake tools and inserts. From the little I've learned negitive rake are specificly for real high horse power and super rigid equipment. Obviously picking a tool holder that takes only some of the really expensive tips would be a mistake too. I haven't really answered the OPs question about tool sets for a lathe, I'm not sure there is just one answer. Maybe just buying tool holders that take your average triangular screw on carbide tips from a well known manufacter and using their carbide tips is about all I could recommend. It would be easy to spend way too much and end up with over specialised tooling that would only do one job.
I'll also add that buying the best you can afford goes for any cutting tool, Drills,taps,dies,reamers etc. You do get exactly what your willing to pay for. If you live outside North America then some of the brand names I mentioned probably wouldn't help you very much. Getting a proper catalog from a large industrial machine tool supplier would help a lot. Most of the bigger and well known carbide manufacter's have volumes of information about how to decide what you need. But you have to remember most of the information is for high volume part production.
After rereading what I've typed I'm not sure I've helped anyone.
Pete