Pic rel is how you may want to model and texture your branches.

As for the log/trunk, I suggest to use Bezier Curves > in the side panel thingie go to Object, Geometry and give it depth, play around with resolution and shit, sorry it's late I don't remember this part too good > in Edit Mode extrude vertices as needed > still in Edit Mode, and with a vertex selected, hit Alt + S to adjust the size of that vertex > once you're satisfied with the shape of the log, go to Object > Convert to Mesh > give it your bark texture (the converted curve already comes UV unwrapped)