Are the best conductors are usually solids, liquids, or gases?
Solids are typically the best conductors of heat.
I'm assuming that you're referring to heat conductivity.
This comes back to the arrangement of particles in solids, liquids and gases.
The particles in solids are very closely packed together, (picture sardines in a can). Liquids are a bit further apart and actually have enough space to slide over each other. Gas particles are relatively far apart and can move about freely.
For heat to travel through a substance, it has to pass from particle to particle.
When heat is being applied to say, a metal block, the heat will be able to travel through the entire block quickly. This is because the particles are very close (basically touching), so heat is transferred from one particle to the next fairly quickly.
In liquids, the particles are a bit further away, so it would take a bit longer for heat to be transferred from one to the next.
In gases, the particles are very far apart, so it takes a long time for heat to get to all of the particles.