Tapping into unused Arduino pins with a shield in place
Last time I looked the Sparkfun Speakjet shield did have stackable headers? Anyhoo aside from that moot point- It depends on how permanent your project is.

If you want to be able to use the Arduino again with different projects or shields - it's definitely recommended you get some stackable headers because of the cheap cost and ease of use. 

If the project is relatively permanent and you don't intend on using the Arduino again in another project, soldering the wires on might be better for you, it will be cheaper in the short run and will be affective for making good connections - it's just fiddly to do and not the most professional looking way of hooking stuff up.