My personal favourite atm is the Cu Sidhe. They may not kill as fast as other pets, and their lack of magic can slow things down sometimes, but their survivablity is amazing. They heal themselves, they heal you, and they'll even rez your 1 slot pet if it dies
If I had to pick just one pet it would be the Cu. Great for lazy tamers
As for best overall multi-purpose I would have to pick Mare/Rune Beetle combo. The beetle tanks really well and has wicked poison, and both are strong magic users. Just make sure the beetle goes in first as the Mare can't really take the hits from tougher monsters.
But as others have said, it depends on the situation, which is why pretty much every tamer has a variety of pets for different tasks.
To give you an example, fighting Swoop with a Cu will take forever, and if it flies on some rocks you are stuffed because the Cu hasn't any magic. Take a Mare/Rune and Swoop goes down in half the time, even if it goes out of melee range.
Hiryus are great, but I think they're ugly, which is why I don't use them.
Dragon/WW are also great, but they are so big they often get in the way. Although before the Rune Beetle appeared my favourite combo was Mare/Dragon.
If I was told I had to clear my stable and only keep 3 pets, it would be a Cu Sidhe, Mare, Rune Beetle