Though even an out-of-date Linux distro is going to be safer against malware than Windows, keep in mind that it's almost impossible to keep one of the major distros updated with security patches via dialup. I tried that with my father in law's computer for a couple of years, setting up a cron job to dial up automatically late at night, every night, and chip away at the downloads. It fell further and further behind.
Other than the fact that I don't know if any of them even support dialup, a Chromebook seems ideal for this application. Updates are smaller and less frequent, and ChromeOS is strongly hardened as compared to a standard distro, so it's less worrisome if they miss some. Chrome Remote Desktop would enable you to take control of the machine when needed (that actually works on any platform) and while it's painful at dialup speeds I have used it successfully.