Your assumption that you have to take your host's nameservers and replace them at your Domain Registrar's website is not quite what you need to do.
First: You do not need to change the
/etc/resolv.conf file on your host. That is the configuration file your host uses to resolve all internet domains/hostnames, not just your own. The ip-addresses 18.104.22.168 and 22.214.171.124 are public DNS servers provided by Google and suitable for most configurations. The configuration should look like:
Changing nameserver records is what you do when you run your own nameserver. Normally you do not need to run your own nameservers and you shouldn't try before improving your understanding of DNS.
I think that what you probably want to achieve is that people using for instance
www.yourdomain.com end up at your VPS and e-mail addressed to
<someone>@yourdomain.com also gets delivered to the mailserver you run on your host.
That is mostly updating the DNS records for www.yourdomain.com ftp.yourdomain.com etc. Typically your registrar provides a management console where you can do that yourself and your domain uses the nameservers from the registrar.
In that management console you enter the ip-address of your VPS as the
www.yourdomain.com and for all other DNS names you might want to use.