The majority of those suppliers provide boron-impregnated plastic, which is fine for e.g. shielding spallation neutrons from a medical linac head. Reactor shielding is orders of magnitude higher, so material damage is a real concern. Not to say that people can't or don't use that material, but it is not the most cost effective stuff.
Frankly, the best neutron shielding in the world, on a per-cost basis, is water with borax. I don't know why people don't use this more. We used to use stacked bags of borax as neutron shielding when I built a fusion reactor (non-self sustaining, of course), and we had more than enough shielding to handle 2.45 MeV neutrons for under $1000.
So in this reactor design, the neutron shield would be quite thin, if that drawing is to scale I'd say like 30-50cm? in that case water in borax wouldn't be dense enough right?
A cool thing about the shield being liquid is that you could theoretically replace it while it's running. It could make the neuron shield double as the heat transfer medium too.
Of course I'm a total layman so this is just highlevel blabbering.
