Some adapters allow at most a 32gb microSD. Others accept 2 x 32gb, formatted correctly. With some adapters you can go up to 128gb, but the PSP menu becomes very slow, and corruption of the microSD during saving or during file management (rename, delete, copy and paste etc.) is more likely, and so you would lose the whole content of the microSD, isos and saves.
I recommend, as in my case, 2 or 3 32gb microSD (maybe with the corresponding adapters, which are very cheap) to alternate when needed, and containing different categories of games or emulators: this is just my personal preference, the choice is yours...