It is not a bad starting point, so it should be OK to use as a general idea. Although I'm not sure how much someone without any physics or particle physics background will understand the idea of something that "... acts between particles with color... ". And I am not sure if the Higgs is solely responsible in giving all particles their masses.
Have you looked at http://www.particleadventure.org/ ? It has a more extensive explanation on elementary particles at .... er ... an "elementary" level. They also have several charts similar to this that you can download.
Hm, well, I'd cancel the word "force" as one of the first thing from my dictionary when entering the relativistic realm. Neither classically (i.e., mostly electrodynamics) nor quantum-theoretically forces make much sense anymore, but the most important concept one has to learn about is the field description of interactions. It's the key issue of locality of interactions that lets us formulate the most successful theory created by human mind ever, the Standard Model of elementary particle physics.
Also of course fermions interact with bosons and fermions as do bosons. That's why it's called the interaction, and it must be like this since due to translation invariance of space and time there's energy and momentum conservation. So if bosons "excert forces" on fermions than also fermions must "excert forces" on bosons. As I sad, I'm no quite happy with using the force concept of non-relativistic physics in this context.
In the very left corner, I don't understand, why they say the differen neutrino flavors are stable or become less and less stable, respectively. Neutrinos are pretty complicated objects, given that they never occur in their mass eigenstates (which admits to interpret them as particles) but are created in their flavor eigenstates states and thus are oscillating. Strictly speaking they make only sense as internal lines in Feynman diagrams, i.e., you have to consider the entire process of creating the neutrino and measuring it in some reaction again.
On the upper left corner one should more carefully say that the Higgs field provides the fundamental mass of the fundamental fields in the standard model. Most of the mass of the matter around us is, however not provided by the Higgs field but is "dynamically generated" by the strong interaction (only about 2% of the proton/neutron mass is due to the Higgs mechanism; the entire rest is due to the strong interacion). This is a very complicated issue, not fully understood today. That it's right, however, we know from lattice-QCD calculations which reproduce the observed hadron-mass spectrum at the few percent level of accuracy.
The diagram may be a help for rote learning some facts about the Standard Model, but this is an approach to physics which is against the spirit of this most fascinating subject! The particle-adventure website quoted in #2 is way better.