Well, things I like. I like a little bit of everything.
I like anime and manga, especially shonen/action series.
I read a lot, almost exclusively fantasy books.
My favorite animal is a badger, so anything with a badger on it is a definite win! I also love cats.
My favorite fantasy creature is probably a hippocampus, with mimics coming a close second.
I am an avid gamer, both video games and tabletop games like D&D.
Regarding postcards, I don't really have a particular preference. I love all manner of beautiful or interesting things, be they landscapes, drawings, or colorful patterns. I will be happy with any sort of postcards. I love supporting independent artists too, so if you or your friend make postcards, send me those (even if it's not professionally printed, I don't mind)!
I do love weird things like aliens and Lovecraft, horror art such as that of manga artist Junji Ito, or things with a Tim Burton-esque style. I would be terribly excited to see something like that in my mail box.
Food postcards are always so beautiful, especially when they are showing off local treats! I love tea and doughnuts, so those would also make me smile.
As for what to write, anything! Tell me about your day, or your pets, or some fun plans you have coming up! Just write something! I think getting to read the postcards is as fun as seeing what the picture is, so just fill it up with whatever!