Fernet. Balsa is by no means the standard wood, there is no 'standard' wood. Just about any wood can be used.
Setting aside all the build advantages and disadvantages of the various woods, the only attribute of the wood that affects the swim of the lure, is its density.
For a lively lipped crankbait with a lot of action, a light wood is favourite. If you want a more subtle action, go for something a bit heavier. The light wood allows you to group the ballast in one place and control the centre of gravity, the pivot point for the action. The tail of the bait, being very light, has less inertia and moves easier.
With a heavier wood, the tail would have more inertia and would give less movement.
Gliders have different requirements. As I don't know much about gliders or other types of lure, I will leave that to someone else to explain their density requirements.
There are many other attributes of wood to be considered in the selection process. How easy is it to work with, how easy is it to drill, seal methods can vary too.
I'm sure I have missed a few points. There have been several threads discussing wood selection. Try a search on the name of the wood you are considering, to find opinions.
Got carried away again. Yes, it is a wobble thing.
Dave