Win 95 and 98 were like Win 3.x - they booted to DOS, then ran Windows as a program which presented a GUI. In Win 3.x, DOS was explicit (you installed DOS, then installed Windows). With Win 95/98, Microsoft integrated the Windows and DOS install into one to try to make it harder for DR-DOS to compete. But it still ran a modified version of DOS under the hood.
Anyhow, bottom line is neither 95 nor 98 are very good. You're basically running Windows programs on top of Windows which is running on top of DOS. Not very stable nor reliable. The multi-tasking is cooperative. Windows hands control of the CPU to a program, and kindly requests the program hand control back in x milliseconds. If the program doesn't or it crashes, then Windows never gets the CPU back and the computer freezes. If you weren't into computing during those days, it was really bad. Rebooting due to a crash once or twice a day was normal. That's why we have all sorts of cute names for ctrl-alt-del like "the three finger salute" (ctrl-alt-del would cause the motherboard to initiate a soft reboot after a crash).
For that reason, if there's any way to get the legacy games to run on Windows XP or 2000, that'd be much better. Those two OSes are based on Windows NT, which uses pre-emptive multi-tasking. Windows always controls the CPU, and controls how much CPU time a program gets. If a program crashes, only the program crashes. Windows and your other programs keep chugging along. It was common to go weeks or even months between crashes on XP, and most of the crashes were due to buggy drivers. 512 MB of RAM will be fine for XP. 256 MB is a safe minimum (with modern anti-virus).
But if you must use the DOS-based Windows, 98 (specifically 98SE as others have mentioned) is preferable. The last DOS-based Windows was ME, which was considerably worse than 98. Lots of ambitious new features like built-in backups and system restore which didn't quite work right in their first iteration and just slowed the system down.
A better choice IMHO is a newer computer with Win 98 or XP running in a virtual machine. Processors and GPUs from back then didn't throttle down under low load like modern processors. So your vintage system is probably going to burn around 150-200 Watts continuously. Compared to about 30-50 Watts for a modern system. If you use the computer for any extended period of time, that extra power draw is going to translate into an extra tens of dollars of electricity per year. After a few years, you'll have frittered away enough money on extra electricity to buy a decent new GPU. Some old things just aren't worth bringing back to life again.