Vanilla sugar is incredibly easy to make. Store a whole vanilla bean in a jar of sugar, shaking it up every so often, until the sugar is vanilla flavored. That's it. The time, I think, would depend on your bean and your taste.
I'm not familiar with the naming conventions for sugar in the UK so I apologize if I become patronizing.
Granulated sugar is the every-day table sugar here. It's what I grab a spoonful for my cereal and such, and it is the kind used in almost all of the baking I've done. Is caster sugar what you usually have around?
Caster sugar is called "super-fine" sugar in the States. It is finer that granulated sugar but not as fine as powdered sugar (icing sugar for the UK right?).
Honestly, I can't say that I've ever bought any as I usually only see granulated and powdered, but Wikipedia tells me that "Castor sugar can be prepared at home by grinding granulated sugar for a couple of minutes in a food processor."
That being said, if you're just beating it into butter than I would think the caster sugar should be perfectly reasonable for the job. Though I agree with bikeboy that you should go by weight if you use a substitue.
Running around This Site, I found that there are aprrox 7oz(200g) per cup granulated sugar, and 6.5oz(190g) per cup caster sugar. So you would actually need more sugar if using caster sugar, as it is less dense. Obviously not a lot though (200/190=1.053).
Best Answer
In general in recipes measuring by weight, you can use the same weight, as 50g of one kind of thing is usually the same amount as 50g of another kind of the same thing (in this case sugar). With volume measurements this is not the case, as certain kinds of things will pack into the measuring cup differently (flour is notorious for packing, for instance, and no two cups ever seem to come out the same).
In your specific case, however, a direct substitution may mot work as desired. Confectioners or powdered sugar often has a small amount of cornstarch mixed with the sugar to prevent clumping. Its possible that a no-bake style cheesecake recipe may be relying on that, so you may want to substitute a few grams of cornstarch for some of your caster sugar. I would try 45g sugar and 5g cornstarch.