If you like the Estonian OÜ approach of corporate tax applied during profit distribution, then setting your legal residency in
Estonia is probably the easiest. No need to involve Cyprus in the solution. Estonia considers you a tax resident as long as you have a registered legal residency in Estonia, there's no need to spend any time in Estonia. Just rent a small cheap apartment there and register your residency in it. Maybe stay a couple of months there in the summer, it's beautiful.
It's similar in
Latvia, so you could set your legal residency in Latvia and create a Latvian SIA instead. The Latvian corporate tax is an improved version of the Estonian corporate tax that actually allows you to use your company as a tax-free holding to a good extent, since it allows you to sell shares in subsidiaries tax-free at a corporate level after 36 months of holding those shares. And if you are tax resident in Latvia when distributing the profits related to that sale as
dividends, you won't have to pay personal income taxes on them either. This may not be relevant if you don't plan to use the company as a holding, but I'd keep an open mind about it. If you were to sell shares of a subsidiary of an Estonian OÜ, you would have to pay corporate
income tax on that whenever you distribute those profits as dividends. Also, Latvia seems to be a bit more flexible than Estonia in terms of what can be considered a business expense, and withholding taxes are usually 0%, so there's that too.
Both Estonia and Latvia give you an identity card that you can use to sign government related things digitally, which makes it easy to do things remotely if you are traveling. You can use the Estonian identity card to sign things in Latvia and vice-versa. If you get legal residency in any of these two countries, you will be able to open bank accounts in them very easily.
In any case, whenever you decide to distribute profits from the Estonian OÜ or Latvian SIA as dividends, you will have to pay 20%. There's no way around that, except in that 36-month thing I mentioned before or if those profits come from a subsidiary and have already been taxed there.
I think Latvia has the cheapest and simplest setup in the EU with company, residency and
bank account all in the same country. Generally it's not tax free, but in some cases it can be. Estonia is a bit more digital than Latvia, and sometimes you can use English in official documents. In Latvia, not so much, but it's still better than most other EU countries. Also, Riga's airport is better connected than Tallinn's airport. If you are not an EU citizen, getting residency in Latvia is easier than in Estonia.
Alternatively, leave Europe. The UAE is a decent tax-free option if you will be constantly moving around.