Material for control rods for thermal reactors (LWRs) consists of B4C and Hafmium. Both are thermal absorbers - that is they absorb low energy neutrons in reactors that maintain criticality using thermal neutrons. Hafnium control rods have had swelling problems in commercial reactors.
Berillyium is a moderating material and makes the nuclear reaction go faster. In an LWR, it would displace the water and slow down the reaction owing to its high atomic mass - however, it would not be used as a control rod.
I believe stainless steel was used for fast reactor control rods which use fast neutrons (thermal neutrons are slowed down with a moderator, like Be, C, Heavy Water D2O, ZrD2 ZrH2 and water H2o).
BeO is an excellent moderator and has been used in India for example. It was studied extensively in the old days in the US.
Alpha emission in Be is actually a good thing because alpha-N neutrons allow for a safer startup, providing a better source of neutrons to detect approach to critical. It is bad however from a transportation standpoint if you load it close to Plutonium for example - however, alphas are easily shielded.
Zirconium is a cladding material used to protect fuel. It can be mixed with fuel to in Uranium - Zirconium allows, or Zirconium Hydride or Zirconium Deuteride can be used as solid moderators (spaceship applications). ZrH2 is lower density than H2O so is normally not used otherwise (why not just use water).