a way for correcting the problem with triangles in your mesh. you can use the retopology tool to paint new verts over a sloppy mesh like a metaball structure thus changing the topology but not the basic shape of the model.
if you want to just click and hold the mouse to push and pull, select Draw mode in the sculpt panel and turn on Airbrush
At this point the most logical workflow is to use your quickly sculpted mesh as a template for the final, well-edgelooped mesh
With that on, as long has you have the mouse button pressed, it'll keep pulling outward. Shift clicking will push the mesh inward. I find Grab to be the most intuitive for gross reshaping, and to me it feels most like manipulating actual clay.