ccTLD's for countries that are members of the EUB usually have pretty strong privacy protection, especially if you are buying as an individual.
.de (Germany) is probably the cheapest (3-4€) but if you're not a resident you will need the registrar to arrange a mailing address for you for a small fee. Still going to be a pretty low price.
.nl is another cheap option, without any residency requirement.
The only issue with both is that you can only buy for one year at a time.
The owner's details in the registry are never published. Legit requests in case of abuse etc. need to go through the registry.