Heck, I'd do all three, and just give less XP to slow the PC's progress.
Maybe chose an adventure from
Adventure Begins that will lead the PCs to the Wildsgate area. (The first adventure,
Black Pearl, is a personal fave, but it doesn't really lend itself to travelling to Wildsgate.) One of these shorter adventures should get the PCs enough XP for about halfway to level 2 or so.
Then you can do
Vault: by the end, the PCs will be solidly into 2nd level which is a perfect segue to
Into the Wilds, which has some slightly tougher combats that a 2nd level party would be well-suited for. At the end of
Wilds, they'll likely be 3rd or even 4th level.
Heck, you could even have the
Vault cave be a few miles east or west of Wildsgate.
Maybe someone in Wildsgate needs to have you investigate the ogre located "up the road a stretch"....multiple plot threads at once can be fun.
SPOILER:
Just be aware that both
Wilds and
Idylls contain a vampire that may or may not give the players some headaches (or, should I say,
neck-aches), so you might not want to run both of those two particular adventures due to redundancy.
Alternately, you could change some background elements and have both vamps be part of a coven that's in the area. Lady Aborn (Wildsgate's antagonist) could even be a vamp too--or striving to be one. Ooooh, I love conspiracies.