My LHBS sells whole hops, hop pellets, and hop plugs. Is there a way to know which this recipe calls for, and is there some sort of conversion formula between the different forms?
There is no way to know anything about this recipe as no IBUs are given. You also have no alpha acid levels given so its tough to know how much you'd need to adjust the hops you buy to the hops in this recipe.
I'd say just go with pellets as that is what the majority of homebrew recipes are built around. Go with the amounts as written. Taste it then make some adjustments for the second round of brewing it.
To my knowledge there is no real functional difference between whole flowers, plugs, and pellets. I have used them all interchangeably.
I would suggest just using pellets or whole flowers. How much you use should be specified in the recipe. As Brewchez rightly suggests, you can't hit an IBU target without knowing what that should be and the alpha acids of the hops. The latter is listed on the hop package. The former, well who knows.
You will need to enter the recipe into a brew calculator or figure it out by hand in order to hit the IBU target (whatever that is).