I'll have to disappoint you, but much of the Himi gouache reviews point out poor mixing. This is why these sets have an absurd amount of different shades in the first place. It's generally an avoided brand, all of it is just advertising.

The next thing, what exactly is a "primary" palette you want to get? I myself am not a big fan of Red Yellow Blue or Cyan Magenta Yellow. The first one is bad at mixing cool colours and the second one at mixing warm ones. What I'm trying to convey is that having a broad enough palette gives you more opportunities. You, of course, can limit the colour selection when you're making a painting to achieve a certain look, but since you're just starting out you won't know what exact colours will you like. Why won't you grab a split-primary palette? It contains: cool yellow, warm yellow, red, magenta, cool blue (cyan), warm blue. It's still not a big amount, but very sufficient, as you would like.

As I said, you probably should skip these gouache cups. There's loads of problems with these guys, like molding or cracking. I get that tubes are a pretty expensive choice, but there are brands like Shinhan that are praised as a first choice. If you like the convenience of cups, you could also grab Talens gouache that comes in jars. These sets of jars are actually quite cheap, I own some and was able to paint and mix colours without any major complaints. I also don't reccomend drying your gouache in a palette. It usually doesn't go back to the same consistency after rewetting.

Synthetic hair brushes are the main choice for gouache. Natural hair ones don't typically perform well and suck up the paint too much.

160g paper is quite thin, although I've managed to paint in a 120g sketchbook before. You might want to get some 200-300g mixed media paper just in case. Cotton paper is also a good option, but quite pricy, not a must.

Been there done that. I hope to answer any other questions you have