How to limit cache of internet browsers?
There's no way to limit the cache of browsers or apps, however you could use one of many cache cleaner apps to sweep the cache/temp files in one stroke.

Take a look at Dolphin Browser as well - it has an option to store the cache on the SD card, so that will eliminate your space problem. There's also the option of clearing the cache/history each time you exit the browser. Also has sync, extensions and Flash support (depending on your device).

BTW - I don't think Opera Mini stores a cache as Opera Mobile does. Opera Mini does however store pages in folders specified by the user.