Leptons and quarks are all elementary particles.
There are 6 leptons: electron, electron-neutrino, muon, muon-neutrino, tau, tau-neutrino.
There are 6 quarks: up, down, charm, strange, top, bottom.
Hadrons are made out of quarks. There are two families of hadrons, mesons and baryons.
Baryons are made out of three quarks. Mesons are made of one quark and one anti-quark.
Examples of Baryons are the proton and the neutron.
Fermions are particles that obey Fermi-Dirac statistics and bosons are particles that obey Bose-Einstein statistics. Mesons are bosons while baryons are fermions. The bosons you've probably heard about recently are the gauge bosons. They are the mediators of fields in quantum field theory. There is the Higg's boson (Higg's field), the W+ W- and Z bosons (weak force), the photon (EM field), the gluon (strong force), and possibly the graviton (gravitational field).
Now, if you take anti-particles into account, you'll end up with 12 leptons and 12 quarks (each one has a corresponding anti-particle).
Furthermore, some propose the existence of a fourth neutrino flavor (or type). They call it sterile neutrino.