What is the reason behind choosing the specific elements used for the synthesis of heavier elements?
There are different strategies for synthesizing superheavy elements. 

Two of the main strategies are referred to as "hot fusion" and "cold fusion". 

The first two reactions are good examples of the "hot fusion" strategy. I will focus on these two reactions, as the other two are much older and I don't think they are good examples of current thinking.  

Experimentally, a very heavy element target (the Es or Bk in the first two reactions) is bombarded by an ion beam of the second element.  The target element is choosen on the basis of being very heavy, availible and not rapidly decaying. 

$^{48}_{20}\ce{Ca}$ is choosen for a very special reason.  This is not ordinary calcium.  The most common isotope of calcium has only 20 neutrons, but this isotope has 28!.  It is extremely neutron rich, espeically compare to other relatively stable isotopes in this mass-range of the periodic table.  $^{50}_{22}\ce{Ti}$ is also very neutron rich.  

Why are neutron rich nuclei chosen? There are two reasons for this:

First, confining many protons in a small space causes electrostatic repulsion.  As atomic number increases, the stable nuclei deviate further and further from a 1:1 neutron:proton ratio, because having more neutrons keeps the protons further apart and decreases electrostatic repulsion energy.  

Secondly, you will notice the asterisk (*) in the 1st, 3rd and 4th equations.  This denotes the compound nucleus which initially forms in the fusion reaction.  It is an extremely ($&lt;10^{-21}$s) short lived intermediate state, not the ground state of a nucleus, but more like a highly excited state.  It's formation is not considered creating a new element.  It is critical to the strategy of forming an element that the intermediate state loss energy through neutron "evaporation".   Notice that in the second equation, the step of the neutrons evaporating is shown, while the intermediate state is not shown.  Generally speaking, in the hot fusion strategy, 3-5 neutrons will evaporate to cool the intermediate state.  

For further reading see:

Future of superheavy element research: Which nuclei could be synthesized within the next few years? and

The discovery of the heaviest elements Rev. Mod. Phys. 72, 733