I use sponge cake almost exclusively for my family. It is not as delicate as some say, but it has its quirks.
Some tips for torting:
Don't use cake leverer (the wilton type, I mean). Use either fine serrated knife - the micro serrated knife works best, don't use cheap bread knife with "big teeth" - or use the knife to cut around your cake, 1/4 inch deep only and cut with a floss - take a length of doubled white thread around your cake, cross the ends and pull - the floss cuts the cake. This works best for round cakes.
After you cut the layer, slip cake board or cookie sheet between the layers to lift the top layer of.
When cutting with a knife or making 3D cakes (you can use sponge cake for this as well, up to certain size), let the cake for an hour in freezer. It cuts easier.
Here (Czech republic) is sponge cake a classic. When you order a cake and don't say anything else, you get sponge cake. Some bakers feel it is easier to bake 1/2 layers instead of cutting the cake. I personally bake "full height" and cut 4 layers.
For the texture of the cake: It is difficult to give advice, because the flour is here very different from US. Generally, even if you use cake flour, give per cup one tablespoon flour less and one tablespoon of potato or corn starch instead - both work very similar. You get finer but somewhat firmer and more forgiving consistency of your cake. Try it beforehand, bake a small cake for your family or friends.
Let me know if you need more help.