Which ones are the best systems to place my trading companies HQ and subsidiarirs?

People tend to say it scales off population and system output.
Generally I favour my home system for a subsidiary more now, since all other trading companies can potentially benefit from the unique trade upgrades, but I could be wrong there too, there just is no clear up to date dev approved message on this.

And not really.

I would also recommend luxury resource planets or one lane away of those as they will be traded on the routes.

You can read about the trade system in the original blog post.

The relevent portion:

Income

Hard point

A trade hard point is either a Branch or an HQ. The income generated will be centralized on these systems, and modified significantly by the route's length. What contribute to the income is then:

• The hard point's system itself
• The neighbors of the hard point
• The length of the trade route 

The income will be  and  on one hand, and Luxury resources on the other hand. The FIDS part will be mostly based on systems stats, whereas the resources income will depend on the spatial localization (a hard point or neighbor needs to possess a deposit for it to contribute to the trade income).

All these incomes will be modulated by the route's length.

Systems on route

The systems on a trade route won't directly contribute to the trade income, but will benefit from being situated on one. Each node traversed by a route will receive a  and  bonus based on the system's development and modulated by the route's length.

Greetings,
dust-producing systems are generally a good choice for a commercial company. Then, the distance between the headquarters and the branches determines what the branches will produce as dust, but the further away they are, the more likely you are to see the communication channels cut off by an opponent. I may be wrong, but it seems to me that this is the basis for the operation of commercial companies. I will not be able to say  certainty if the presence of rare resources on the planets where they are located improves their dust production. Good luck!

As others said there is a risk for disruption on long routes, but i like to have the routes to cross as far through my territory as possible, as all system on the route also profit/enrich the route.

Resurces of systems in between also get a small boost as well as food on those systems.

Is the amount of different types of luxury deposits resources on a system an important factor here? 

In terms of best systems since the more there are on a system the more are traded hence also more science and dust produced from it.

If so i would suggest you make these systems with high amount of different luxury deposit resources to be HQs and those with fewer to be subsidiaries, given that you don't have two or more of any involved systems producing the same resource. That is to say the higher the variety of Luxury resource deposits the better your trading rewards as returns in science and dust as well as the leveling up and growth of the trading companies.

Well there are 2 types of company upgrade. Science and Dust or Luxury and Dust.

Planets that make most dust are probably those that have luxuries on it and toxic, gas.
So imo you should put them where rare tier 2/3 luxuries are to upgrade your system fast.
Also worth mentioning that in my experience playing game on FAST pace makes trading companies kinda useless. I generate more form system and upgrades cost tons.

Yep, as you said Koxsos, there's no clear explaination for trading, we have to try out what works and what doesn't works. Trying, learning, succeeding ^^ that's a good way to approach a game, instead of showing everything from the begining.