I find that Beginning ArcGIS for Desktop Development Using .Net (Publisher) to be useful. They break down the operations into decent little exercises that are fairly practical. Plus, you can download their code from the website.
If you are better with Java, you can also do ArcObjects in that language, too. I don't believe there is much support for VBA anymore. I think that was mostly MapObjects.
You might find that learning python and ArcPy to be a good starting point to get the flow of ESRI processes.