Go ahead and bake your angelfood cake, mix up your pudding, and whip your cream. These can be stored until you're ready to assemble the trifle.
I've made angelfood cake from a box and from scratch, and the difference isn't major- here you're combining it with so many other flavors that any such distinction would be lost. Purchased pre-made angelfood cakes will do, but tend to be a bit dry and sometimes taste off. Pound cake may be traditional, but I prefer angelfood because it's lighter, more absorbent, and complements the berries better.
I used a trifle bowl (purchased at Target for $14), but you can use any bowl. Glass is preferable, because then you can see all the pretty layers.