I would probably say "postcard lover" or "postcard fan" since often when creating such a phrase we would use the singular. One thing to be a little careful about with the word "lover" is that it does have a second meaning that implies intimacy between two partners. Having said this, many people quite happily use the above phrases without concern. Wade's suggestion to use "lover of postcards" clears this up completely.

Hello Aude, It's not a silly question! You are correct that your 3rd option sounds the most natural. I would recommend 'lover of postcards' or 'fan of postcards' or even 'postcard collector/collector of postcards' Hope that helps, Wade.