I'm not a physicist (so take this with a grain of salt) but I have spent a lot of time trying to find an answer to this question. If you interpret the physics before Spontaneous Symmetry Breaking as more fundamental, and you treat the antimatter fields as distinct, then I think you can reasonably claim that there are 30 fundamental fermion fields. Specifically, in each of the 3 generations, you have:

1. The left-handed lepton doublet field, and the antimatter equivalent. 2. The left-handed quark doublet field, and the antimatter equivalent. 3. The right-handed electron singlet field, and the antimatter equivalent. 4. The right-handed up-quark singlet field, and the antimatter equivalent. 5. The right-handed down-quark singlet field, and the antimatter equivalent.

The bosons are more confusing to me, but I think a reasonable person might say that there are 16 fundamental boson fields:

1. The four scalar boson fields. 2. The eight gluon fields. 3. The three W boson fields. 4. The B boson field.

The B boson couples to every fermion (via hypercharge), while gluons only couple to quarks (via color) and W bosons only couple to the doublets (via weak isospin).