I've heard good things about Estonia as well. Don't forget, merely incorporating a company in a different jurisdiction will NOT mean it is resident there.

Establishing companies in different jurisdictions can be a viable way to run (internet) businesses, but care needs to be taken in various areas.

If you have limited understanding about business and international structuring, go with a South Korean company. If you want to use a foreign company, you will probably need to register it in SK regardless. Especially if you're the sole director/shareholder and running it from SK.

'Offshore' havens often serve very specific purposes, i.e. holding of assets or stakes in companies, as a tax neutral special purpose vehicle to easily structure a joint venture, etc

If you take the foreign route, talk to a (South Korean tax) lawyer! That way, you can get it set up properly. You might get pummeled with fines otherwise.

The way it was explained to me is that you need to physically travel to Estonia once, to become an Estonian e-resident. From then on, you can deal with the Estonian government exclusively via the internet. You get access to a very large amount of the services they provide to their real citizens. Not all, of course, but starting a business is on the list.

Looks like you need an id card, and it looks like this is something issued to Estonians. If the question is whether anyone (not just Estonians) can easily and quickly setup a company there, the answer looks to be no.