If you have dialup Internet, that means you have a phone line. Bring a telephone with you, that is the option that has the best chance of being compatible. "Compatible" in this case meaning your old wired telephone will be able to initiate and receive calls with modern phone users.
Electronic messaging is possible but setting it up can be complex because while you may want to limit yourself to pre-Y2K technology, the people you want to communicate with will not be. Even something simple like email may be difficult to manage if your pre-Y2K system can't handle modern encryption and sender authentication protocols. Your best bet is to log into a Unix or Linux system running modern software and send/receive emails from there. And that's assuming you can either get an SSH client for your pre-Y2K system, or you can find a Unix or Linux system online that still allows unencrypted telnet logins. Failing that, you may need to contact the people you plan to email in advance and ask them to whitelist you so your unsigned emails sent from an unregistered mail server won't be flagged as spam (or blocked outright).
If you can find a dialup ISP who accepts unencrypted POP3 and SMTP connections from their customers, then forwards your emails through a modern mail server that adds the appropriate anti-spam headers, then any of the old POP3/SMTP email clients (Thunderbird, Outlook Express, etc.) should work.
