Well, you didn’t actually post a model…
But anyway I cobbled a test model together based on your screenshot, and unwrapped it in the three ways I would use myself. In the attached blendfile they are stored as UVmap, Uvmap001, and UVmap002. Normally of course there would only be a single UVmap, this is just for instructional purposes.
The first method (UVMap) was to select all, deselect a nice even size and shape quad and reselect it, making it active. Then U for unwrap and choose follow active quads from the menu. Not great but usable… Some overlaps though so not great for painting.
Second method (UVMap001) was to select (face mode) from four axial views (front, top, bottom, back in this case) and choose ‘project from view’ from the unwrap menu for each time. Then go and select all the quads that did not get selected and go to right or left view and project from view for them. This works very well because relative sizes are well preserved. Not connected though - you can do that manually by dragging in the UV editor, or you can use the
Third method (UVMap002) was to mark seams around the edges where a cut would be most useful and choose ‘unwrap’. There is no substitute for experience here - sorry. It’s never practical to try to keep everything connected, the distortion is unacceptable. in this case by freeing up the little sticky out cubes I was able to keep everything else nicely low distortion. Choose live unwrap from the toolshelf or UV menu and you can see what the result of marking and clearing seams is as you go along.
Remember, you are only unwrapping what you have selected BUT all faces are unwrapped even if you don’t do them Blender will and it may not be the best choice. Select all from time to time to see what the whole unwrap looks like.