.cc feels scammy to me at a glance. I like .eu, just don't know a good place to buy the domain and hosting. Like, where is thepiratebay hosted, or some bitcoin casinos or similar
.co.cc is probably what was being referred to. It's not a TLD in itself, but a South Korean company specializing in free web domains provided under the co.cc TOS. Sites registered with these domains will look like x.co.cc, where x is the domain name you provided at the moment of registration. Sites registered here are also removed from Google search results, which you can use to somewhat augment your privacy.
As for the ideal domain/VPS integration you want to use, you're probably going to keep getting vague answers until people know exactly what you want to use the site for. Unless you're involved in illicit drugs, porn, or plan to have a static repository for copyrighted material, I don't think you have enough reason to be concerned about federal law enforcement touching your online content.
I would say just learn how to host your website through the Tor network, People can still access it via the tor2web out proxy.
His site could be down or unusable for inexcusable amounts of time owing to the heavy traffic transmitted over Tor, just saying. Additionally, any interruption in Tor service on his end would disrupt the site.