So for human creation, as in realistic fiction or humans in fantasy or normal fiction, you really want to have a specific defining trait. Humans are complicated. We know that. But for characters, we want them to have dimensions, but also a way we can classify them. For instance; the mousy-brunnette with glasses: quiet artsy type who maybe likes unicorns; the flamboyant gay who likes singing, theatre and skydiving. Your characters can be original, but they also have to have the few eggagerated traits that helps us define them. You can have the jock type be totally into fairies, but you have to make it so that it somehow defines his character (he has a fairy collection, loved looking up pictures of them, wants to be able to wear a tee to school with his favorite types on it).
Fantasy Creatures
These you can have a lot of liberties with. You can go the norm and have a short tempered small dwarf, or a small fairy who loves nature. With this, you really have to make them somehow stand out a bit, maybe not too much in the appearance, but you can also make their personality a little less cut and dry. It may even be more beneifcial to go the exact opposite. What about the super many unicorn who hates sparkles and is allergic to rainbows? Or a tomboy fairy with pink wings who hates animals? The nice thing about creatures is that they can be whatever you want them to be. You cna make them however the heck you want to!
Animals/Pets/Cute Creatures
These can be quite similar to the fantasy creatures, although these I classify as mroe of pets or non-verbal beasts or slightly sentient beings. Most of the time these can be whatever because people have these types of characters from loyal-as-dogs to flaky-as-Townhouse-crakers. If you really want this type of being to be original and/or special, I would pay the most attention to physical appearance and then to personality. The physical appearance can be what attracts people to him/her/it so it really matters. Ex: a ferocious dragon, a cute squid monster with big eyes, a bun-thing with an adorable expression. All these are interesting things that attract a person to think/look at it. Then you can make it have an interesting personality. Ex: dragon who loves pink, squid monster that glomps people, the bun-thing that kills people with cuteness, etc.
All in all, pay attention to your characters. Listen to what they tell you, don't just make stuff up, think of what THEY would do. Make them original. Make them entertaining. Make them classifiable. Make them interesting.
Happy Creating! :)