wow...well, developing your own GIS application is going to be a lot of work.
If you're starting from scratch, I wouldn't even think about it. Otherwise, look at ArcGIS Engine or the ESRI developer's network. With ArcGIS Engine, you could develop a stand-alone GIS application using their base components. They've already developed mapping controls, TOC controls, etc. But, I will warn that the ArcGIS object model is quite complicated and can take a lot to put your head around.
The books Exploring ArcObjects
] detail the object model. It's for Version 8 and they're about to release Version 10, but they haven't published books for the newer versions, and the majority of the info is the same.