You don't need to list any nameserver other than
/etc/resolv.conf. What you need to inform dnsmasq of the upstream DNS server, and it will relay and cache requests to the ISP's server.
If your ISP's DNS providers don't change (they rarely do), you can declare them in the Dnsmasq configuration file (
/etc/dnsmasq.conf), with lines like
server=203.0.113.1. If your ppp or dhcp daemon drops the addresses of your ISP's providers in a file, say
/etc/ppp/resolv.conf, then reference that file in
You'll find instructions for most common setups in the Dnsmasq setup documentation, and the complete list of options in the example configuration file.
If you're running Debian, Ubuntu or some other distribution with a resolvconf package, install it. Resolvconf automatically manages adding and removing entries from the DNS configuration when you connect or disconnect to a network.