Capture should honor the distortion correction in the camera, as well as any corrections from lens firmware. I'm not terribly impressed by other distortion control capabilities.
The basic workflow for Capture is pretty straight forward - work from top to bottom on the right. Start with the Develop section for global adjustments similar to View. Then go to the Adjust section.
In the Adjust section I normally work the menus from top to bottom and left to right. I start with global adjustments and then come back with selective adjustments. The key icons for me are the Color Control Point selection and the Selection Tools (both positive and negative). The Color Control point is pretty straight forward. Just remember that you can size the control points or add control points with no changes to manage exactly where an effect is applied. With Selection tools you can apply any editing step - sharpening for example - just to the portion of the image you desire. I use this a lot for D-Lighting, Contrast, and Sharpening. Apply your crop and final sharpening last.