See my post above. I wonder whether the "like" was for the final comment, "I won't write another long post, at least not yet. ..." :-)
You are getting great advice above from the others. I'll jump in to add a little more ...
"Woodturning: A Foundation Course
" by Keith Rowley.
Keith Rowley passed away 15 years ago, and the book is still a best seller. It is written in UK English. The basics are very well covered, including safety. Many woodturners owe their start to this book. It teaches the use of traditional high speed steel gouges, chisels, and scrapers. (Carbide turning tools would fall under "scrapers", but carbide tools are not mentioned in this book, which predates them. Trust me, it doesn't matter.) The DVD is good but dry. Don't watch it if you're sleepy. You can find many similar videos online.
Carbide Turning Tools:
This thread discusses carbide turning tools. See my post #2 for a detailed discussion about carbide:
Some woodturners feel that carbide turning tools make it easier for beginners to get acceptable results, but at some point the carbide tools limit them from achieving their full potential. If you watch live or video woodturning demonstrations, notice that very few professional woodturning instructors and demonstrators use carbide tools.
Traditional High Speed Steel (HSS) Turning Tools:
High speed steel turning tools require sharpening tools and sharpening skills. The more I use the traditional HSS turning tools, the more I enjoy using them, and the results show it. When I have issues with the HSS turning tools, 99% of the time the root cause is that they are not sharp. What they need is a quick sharpening touch-up. It is so tempting to keep cutting, but you must stop and do that quick touch up. Notice that professional woodturning instructors and demonstrators use HSS turning tools, and they touch them up frequently during their demonstrations.
(Most of the time, the tool holder on my lathe has a mix of HSS and carbide turning tools, and I have no qualms about switching between them. I see no reason to be a purist.)
There are many fine HSS turning tools and turning tool sets, and a few bad ones. You get what you pay for. I encourage you to do your own research and shopping. Here is what I use:
I have the Robert Sorby Six Piece Turning Tool Set and I am very pleased with it. I found it on close-out at my local woodworking store. Even at full price, it is a good buy for quality tools. I would probably buy the eight piece set for just a little bit more. The tools are sized just right for someone starting out in woodturning, and they give you the tools you need to turn almost anything. It includes tools for spindle turning (between centers, like pens and handles), and tools for face turning (like bowls and platters). Future tools that I might buy for myself to supplement the six piece set would be a larger bowl gouge, a thin parting tool, and a wide scraper.
HSS Turning Tool Sharpening:
Do as I say, not as I do... I have a Grizzly wet grinder. It is okay, and I won't replace it, but I would not recommend it. I bought it under the assumption that a water cooled grinder would prevent me from overheating and damaging my nice HSS turning tools. I wanted a less expensive Tormek. The issues with the water cooled grinders is that they are a pain to set up and use. Touch-ups take more time and effort than they should.
What would I recommend? A low speed grinder with the Wolverine jigs. Most woodturners seem to use them, except me. Even better: The same setup with the CBN wheels that @Quickstep
Note: That old Craftsman bench grinder in your garage is not a low speed grinder. It will burn up your tools.
Four Jaw Chuck:
A chuck for your lathe is one of the most useful accessories you can get, especially for face turning (like bowls). I have a Nova G3 set in a plastic case, and recommend it, but shop around. There are many good brands of chucks available.