The answer is not a simple one. It depends on where the end product will be (on the Greenfoot site? as an application? etc.). Other factors may be the amount of data that needs to saved and data compression size. Running your scenario within the greenfoot application, you can save data either to data files or use the UserInfo data storage provided by greenfoot. On the site, you can only use the UserInfo data storage provided by greenfoot. As a stand-alone application, you can only save the data to data files.

Thanks! I don't think it will end up being uploaded to the Greenfoot site, and just kept as an application. How much can I use the UserInfo data storage to save things- like player name, a list of pokemon in party, individual pokemon stats, that kind of thing?

Like I said: You can refer to the UserInfo class documentation for its specifications (as well as how the use the class and what methods are available).