Network
Using a NIC (Network Interface Controller) directly under DOS isn't really recommended, as the drivers tend to take up a lot of memory (200-300 KB is not uncommon), leaving not enough for most games. It makes a bit more sense with a NIC under Windows (3.1+). Note that Windows 3.1 does NOT include network drivers on the installation disks, while 3.11 (Windows for Workgroups) does. It is possible to make it work under 3.1, using DOS-drivers.
Warning
Exposing a Windows 98 computer to the Internet is most likely a bad idea! Windows 98 still contain vulnerabilities that can be exploited from the Internet. However, as the base code was completely rewritten for Windows 2000 and XP, it is unlikely that those vulnerabilities carried over and that someone would be scanning for them today. Unlikely, but not impossible. If you do connect your Windows 98 (or DOS) pc to the Internet, you are doing so at your own risk!
But which cards can you find DOS/Win3.11-drivers for? Well, the easiet is any card based on the Realtek 8139-chip! Unfortunately, Realtek have removed the drivers from their website, which were available up to the early 2020s. They should be easy to find online - or in the download section on this page.