My short answer is:

Your main reason for setting up a charity is probably to provide tax incentives for your donors. So the best jurisdiction is probably the jurisdiction where your donors are.

However there are some exceptions where this doesn't apply. For example, you may be setting up a charity solely or primarily to access Google Ad grants.

If this is the case, then "shopping" for the jurisdiction with the least regulatory overhead would make sense. It would also need to consider whether the process requires someone with an address in that country.

I don't know the answer to this, and given that it's something of an edge case, I don't know of anyone having done this comparison.

I've never done this myself, but here's bits of info I've absorbed through osmosis by working with people who have.
-Budget about 50-100 hours of work for registration. Not sure which countries require more work in this regard.
-If you're working with a lot of international partners, some countries have processes that are more recognized than others. The most internationally well-known registration type is America's 501(c)(3) - which means that even if you were to for example work somewhere like India, people are accustomed to working with 501(c)(3) and know the system. Less important if you aren't working with partners.
-If you are planning to get donations from mostly individuals, consider where those individuals are likely to live and what the laws regarding tax deductibleness are. Large grantmakers are more likely to be location agnostic.
-You don't need to live where you register, but if you want to grant a work visa to fly in an employee to a location, generally you will need to be registered in that location.

If you're interested in starting a charity you should consider auditing Charity Entrepreneurship's incubation program, and apply for the full course next year. Audit course will have information about how to pick locations for the actual intervention (which usually matters more than where you register for your impact). The full course for admitted students additionally provides guidance and support for operations/registration type stuff.

It’s not strictly relevant, but the Word Bank publishes the Doing Business Report, ranking countries based on how easy it is to do business. Some indicators might be useful to charities, too, like enforcing contracts. Maybe, on average, countries with higher ease of doing business have also higher ease of doing charity.