File vs database? - it is easy. What is database - it is a file. Only it has an engine that knows how to manipulate that file.
If you use file, you suddenly need to think, "what if?". What if file gets corrupted during write. Or what if computer shuts down in the middle of write? DBMS takes care of this issues by issuing all sorts of mechanisms such as uncommitted data files, etc. Now you will need to provide this mechanism yourself.
This is why you should write to file only non-critical data. For example, some user settings. Because if you lost that file, user can re-size controls again but no data will be at loss. Or log file is another good use of file. Because if you lose a log, you can live without. But if you lose months of worth of data...
In your case, I don't know, how user history is important. 300 items is not a large array. You can use XML by creating an object (class) and mark its properties with XML attributes and then use XML serializer to serialize your history into XML
http://msdn.microsoft.com/en-us/library/system.xml.serialization.xmlserializer.aspx
But if it is going to grow and you not planning to age some of it and delete, look into RDBMS.