I'd keep it simple. And either..
1) Apply for an EU Blue Card (gives most advantages)
2) Start your own company (allows lots of geographic flexibility for assignments)
The EU Blue Card gives you full flexibility in terms of mobility (not needing to re-apply for each country for work permits), whereas starting your own company lets you sidestep the labour market entirely and simply work where you want.
In general, receiving a residency permit in one Schengen country allows permit-holders a certain amount of mobility, but you are still bound by national laws.
To move from one Schengen area country to another for more than three months, you will need a long-term visa and/or a permit for that country. If you wish to work, study or join your family in the second country, you may have to fulfil more national conditions. To travel to a country that is not in the borderless Schengen area, you must get a separate national visa and meet all the necessary conditions.
As a skilled knowledge worker, you in principle qualify for an EU Blue Card. The linked PDF explains all the various rights/privileges it offers you - including affirmed ease of mobility within EU member states. It is the most straightforward way to achieve your aim (to live in one country and be directly employed in another, with the right to choose yet another in the future).
The details for work permits do vary from country to country, making a Blue Card a useful thing to have. Note that UK, Ireland and Denmark do not participate in the Blue Card scheme.
Going through the front door for German work permits, which assume residency can make it easier for some companies to sponsor you. Also here more information in German. Work permit regulations usually require substantial effort/commitment from employers which can be a barrier. This could also mean having an official residence in Germany (or wherever), which could also increase your costs.
If you don't want to go the route of an EU Blue Card, and don't want to set yourself up as an official resident of Germany/NL, then start your own business and sell your services to companies that way - no need for complex social security tax constructions, etc. Here is an English-language overview of the requirements for setting up a business in CZ in relation to residency permits, etc. And here's one for NL. Be aware that different criteria regarding size of investment and/or number of jobs created may be applied.