OK these aren't sets you can buy as a set but these are the tools I recommend and will describe why below. I have well over 100 tools and use them all from time to time because I turn a little bit of everything. However 90 percent of my turning is done with this set. Top to bottom. A Thompson parting tool, Thompson 1/2" bowl gouge, 3/4" spindle roughing gouge, Thompson 3/8" detail gouge, Thompson skew, Thompson scraper tool blank ground to a round negative rake scraper, and John Jordan Shear scraper. With this set of tools I can turn virtually everything except hollowing and I do hollow bowls and boxes but not anything through a small hole. This set should work extremely well for just about anyone.
The set I recommend for bowl turning is a Thompson parting tool, A 1/2" thompson bowl gouge, and Thompson round nose scraper and John Jordan shear scraper. With those tools you can turn just about any bowl. You may have to regrind the bowl gouge to do the bottom of steep sided bowls or buy a second gouge and grind it accordingly.
Carbide tool set. With this set I can turn just about any bowl including steep sided bowls, I can turn boxes, platters, Pens, spindles (although you might want a skew for just a few cuts like V cuts for spindles) A thompson parting tool, A Hunter #5 carbide tool for doing steep sided bowls and the bottom of boxes, and a Hunter Osprey. With those 3 tools I can turn an awful lot of stuff. If you turn larger bowls a Hunter Hercules would be easier for roughing, than the Osprey.
I do probably 90 percent of all the work I do with the tools pictured above. The only other tools I use are hollowing tools for doing larger vessels and Christmas ornaments.