These people who say you have to use self-raising flour are *scary*. If
there's leaven in the cake recipe (either baking powder, baking soda, or
eggs beaten until triple volume) then you don't need self-raising flour
at all, in fact it will screw up your recipe. (Caveat: If your recipe
calls for self-raising flour that's the only kind you can use. But I
think self-raising flour is just silly.)
The best flour to use is cake flour, sometimes called weak flour because
it has very little gluten. Cake flour is best because the lack of
gluten makes the cake light and tender.
All-purpose flour is all right, it's a medium strength flour. It won't be quite as tender, but I've used it before with success.
Do not use bread flour, or strong flour. The amount of gluten in it will make your cake tough.
Cakes can be hard. Be sure to follow your recipe exactly for best results.