Consider how you are going to use the data. If there are any reports you have to create, which way would allow you to retrieve and work with the data more easily?
And you don't have to use a date type field. You could just have a Year field and a Month field that are both integers. Then when you actually need to do any kind of expression with it requiring a date it's easy enough to put them together and cast to a date.
And storing as a date with the day number as 1 and just ignoring it is perfectly okay and fairly normal too. In the end this isn't a decision that's going to matter a whole lot (relatively speaking) so I would just choose the one you like best and get it done.
