The most common infection is the one where they turn your computer into a node of a botnet. From there it can consume your bandwidth, launch attacks on other people, or be used to distribute files, such as child porn.
Do you want to be implicated in a child porn ring, and have the evidence sitting right on your computer?
Chances are said Win98 box is off when not in use, and it is very unlikely that there is much of that kind of malware targeting Win98 anyway since it has a nigh-0% install base. What does actually run on it is probably going to be noticed because it's probably running on period hardware and the resource usage will not be nearly so negligible as it is today.
It doesn't have any connection to a network of any kind. I mainly copy stuff over on USB. GOG games don't install on Win98, but if you install them on XP you can often just copy the directory across.
