The one that appears in the opening credits of the feature.
This part usually gets localized if the distributor varies from country to country.

If in doubt only enter those that have credits like "XYZ presents", "A XYZ Presentation" or similar

I don't know why you want us to theorize over hypothetical questions... Give us a real world example and we can start from there.

I would start by entering the production companies in the studio field, since they appear to come from the actual film credits and not from some tacked on opening logos.

Then I would probably enter Media Entertainment and Think Film as media companies, assuming they performed at least one of the following functions: Publisher, licensor or distributor. If you are unsure you can always leave them out.

I would not enter Outsider Pictures as a studio since they were not responsible for the original theatrical release. Unfortunately, how you do it is up to you since the rules make no distinction between original and local theatrical releases, most likely because they were written with American films in mind. But since this isn't an American film, it makes little sense to include them, imho.

Miramax Home Entertainment is the DVD distributor, so goes in the MC field.
Miramax Films is the theatrical distributor and, because they are also a film studio, they go in the Studio field...not my logic, but it is what it is.