Depends on what you mean by "minimum required". You can run Win98 with 32MB or even 16MB
Anyway, 128MB is usable if your budget is really tight
256MB will show a big performance jump from 128MB
512MB still shows improvement but but not as much as 128-256
Going above 512MB gives you bragging rights but shows little or no gain except for a few special applications.
For gaming, the order of priority is graphics card, RAM, processor, assuming that no part of the system is too ancient.