I'm pretty sure there is no vetting process. The only thing to be aware of is that after you set up your agent, you need that agent to understand their responsibilities and do what is required if they receive a take down request. You can be liable for their screwups. So, for example, you can't just turn the DMCA process into some sort of black hole where people who complain send requests and then the agent tosses the requests in the trash and leaves the content up. You need to know what the law requires of the registered agent and the company using the registered agent and comply. Otherwise, if you don't do as required your flushing the $105 (or whatever it is) down a rate hole.
But yes-- it's not a complicated system. Large companies do hire attorneys -- but it's not required.
Oh-- oddly, I don't think you are even required to make the identity of the registered agent easy to find-- but check on that. It will be available at the copyright office, but I've tried to use their search tools... and oy!