So as far as the individual turning tool purchases, this is where I think it is really hard to get out of our own heads. Some turners specialize in finials, so their tooling is catered to that, while others do bowls with traditional gouges and have a good selection there, and others do bowls with scrapers, so they have multiples of those. Some try to be able to do a bit of everything, so have more generalized tools.
I think this is where your own practice, experience, and preferences will come much more into play.
As far as quality manufacturers, there are three that are fairly popular: D-Way, Thompson, Carter and sons. I personally started buying D-Way as my nice tooling, and was so happy with them, that I haven't ventured far. I do have plans to try out some Thompson tools in the future though.
If you want to be able to do small boxes easily, I have been eyeing the boxmaster tools at D-Way. I haven't bought any, but they are on my short list to get in the future, and most are double ended, which makes it really convenient to get two different but related tools on the same piece of steel. This is the one I plan on getting:
https://d-waytools.com/5-8-double-en...ttom-box-tool/
Here is my current inventory of unhandled tools (most being D-way):
https://live.staticflickr.com/65535/...0aa0e38e_b.jpg
I have a separate drawer for the handles:
https://live.staticflickr.com/65535/...ac530a63_b.jpg
For me, the first D-way tools I bought were the 5/8" bowl gouge, spindle roughing gouge, 3/8" spindle gouge, 1 inch skew, and the round nosed negative rake scraper. This gave me some good tools for general use. The second order was when I added the 5/8" bottom feeder bowl gouge, 1/2" spindle, beading tools (I wanted to try them out, they are more of a specialty use, but they work great), parting tool, and the other negative rake scrapers (straight spear point, and curved).
If you want a bowl gouge with a handle already, then the Ellsworth signature gouge made by crown is an great gouge, and I use mine often in addition to the d-way bowl gouge. If you really get into bowls, you may accumulate a whole bevy of bowl gouges with different grinds and flute profiles.
If you get more into finials and the like, look up Cindy Drozda, she has contracted with some manufacturers (I want to say Thompson for many of them) for her specific grinds and profiles.
So I think the biggest thing is for you to get comfortable with your lathe, and try out some different kinds of turnings, and then when you decide that you want to get more into a specific type of turning, buy the tools that are best suited for that. You will most likely also have preferences ebb and wane, so you may end up with a whole bunch of tools of every which kind after a decade of turning, and appreciate each and every one of them!
As a quick personal example: I started with making pens, and did that for a long time, then did some one off random projects, then getting into cups and small bowls. I did this all with Easy Wood Tools for many years. When I decided to try larger bowls, I realized that the easy wood tools weren't the best suited tool, and that is when I decided to get traditional tools and learn how to sharpen, and then once I felt comfortable, I later bought the D-way tools. At one point I wanted to get into hollow vessels, which meant that I needed additional tools as well, so I got the #3 Easy wood tools swan neck hollower, and then also added the Hunter Carbide Badger tools for hollow vessels. I'll probably want to try some finials later, and will most likely get some more specialty spindle gouges to do that. I find it fun to try new types of turnings, and to make a whole bunch of mistakes, and then see my progress over time.
I hope this helps at least a bit!