That winged lion could be a certain type of gryphon. There are many different types of those, all they are are combinations of birds and mammals... the only question is what bird it was based off of...
I would like to join! And by the way, there's a very common an important creature you guys never mentioned--this is the one I would like to be.
Fairies! Yes, in some cases they're depicted as spirits, but then again so are phoenixes in a way... Fairies show a strong connection to magic and nature, and they thrive in the presence of belief.
I'm usually not comfortable with using other people's pictures, but the picture I provide looks kind of cartoony while all the rest look realistic...
It's
this one that's in question, but it looks more like a pixie as it looks more catlike. If a fairy is more mammal-ish, it's a pixie, not just because that's the kind that bites... But the one in this picture doesn't--maybe it's just a rumour. And that's the one I'll be if it's OK.
Also
here's a really neat picture of a phoenix that I drew (well, except for the background)