Copyright is free and automatic from the moment your creative work of authorship was put into a tangible form. You just need proof that you were the original author on some particular date, if it ever comes up. The US Copyright Office has absolutely not idea who is the author; they just took your money, checked that the form was filled out, and sent you the certificate. You're right that copyright may be enforced "all over the world".
Copyright does not protect any "idea" or concept.
Trademark ownership is also free and automatic. Non-registered
trademarks can be enforced in the USA wherever you have actually done business, not just in your "city". You can optionally register a trademark in one or more US states or in the USPTO, and the latter gives you entree to international rights, under the Madrid Protocols...