I like to kick off with a classic (or even cliched) monster, just to ease everyone into the world. It's a good idea to add something new or unusual, but not too much.
My reasoning is that this lets the hunters (and players) come into the first mystery with a good idea what to expect. Something entirely new means the players have to get up to speed on the creature, which is not what you would expect from experienced monster hunters.
So, with that in mind, here's a short list of things I would consider good first monsters:
- Vampire
- Werewolf
- Ghost
- Demon (or demonic possession)
- Shapeshifter
Alternatively, you could just pick a cool monster from a movie and change it around a little (e.g. like the trolls in "Troll Hunter" but they're reptilian, and their weakness is salt instead of daylight).