The answers here are good solutions to your problem, but, IMO, it's the wrong problem to have. I would rather have a good look over the reference before getting down to the nitty-gritty of shovelling vertices around, and work out how to make the job as easy as possible for myself.
If you're modelling low-poly, or low-poly to be subdivided for curvature, then it's rare the surface needs to be manifold - you can model separate parts as separate parts, choosing an appropriate number of vertices in the profiles. In this reference, the parts which are 4,5,and 6-based are conveniently discontinuous, and don't have to be smoothly merged. (A subdivided pentagon makes a pretty good circle)
If you do need a manifold, continuous mesh, for example for printing, then you will probably be higher-poly anyway .. you can choose a number of vertices, in this case, say, 30, as @moonboots suggests, which can be divided by all the profiles you're interested in.
If this case needed to be manifold, just for example, you could start with the pentagon, giving it a 2-segment bevel to tighten its corners. Having extruded that into one of the four arms, spreading the bevels with Loop Tools > Circle, you can Bridge Edge Loops rotated duplicates of the arms together with a good number of divisions to work on the main trunk in a way you would like:
You can then use Loop Tools > Circle again on the open boundaries top and bottom, locking Z so it is circular only in projection onto the XY plane, and extrude the trunk from there.
and then the number of vertices around the trunk is 32.