You are correct that the having the diene in an s-cis conformation is extremely important. Only from this conformation can the Diels-Alder occur. If there is a high concentration of the s-cis conformer the Diels-Alder will likely occur rapidly; if there is a low concentration the reaction will occur more slowly.
In cyclopentadiene, the diene component has no choice, it is locked in an s-cis conformation by the ring. However with acyclic 1,3-dienes an equilibrium exists between the s-cis and s-trans conformations.
In 1,3-butadiene the amount of the s-cis conformation is relatively small (~2%) because of the steric interaction between the "internal" hydrogens at the ends of the chain in this conformation. In accord with this expectation, 1,3-butadiene is not as reactive as cyclopentadiene in the Diels-Alder reaction.
If we replace one of these "internal" hydrogens with a methyl group (penta-1,cis-3-diene), the steric interaction between the "internal" methyl and hydrogen in the s-cis conformation is even greater, further destabilizing the s-cis conformation and reducing the amount present at equilibrium. On the other hand, replacing one of the "exterior" hydrogens with a methyl group (penta-1,trans-3-diene) doesn't cause any increased steric interference in the s-cis conformation and the amount of the s-cis conformer is about the same as 1,3-butadiene. Again, in accord with expectations, penta-1,trans-3-diene reacts at a rate similar to 1,3-butadiene, whereas penta-1,cis-3-diene reacts slower.
Using this information we can make predictions for your compounds. We would expect cyclopentadiene to react the fastest because it is held in an s-cis conformation. In the case of cis, cis-2,4-hexadiene we now have an internal methyl-methyl interaction, which severely destabilizes the s-cis conformation, so there is very little present at equilibrium and this compound reacts the slowest in the Diels-Alder reaction. trans, trans-2,4-hexadiene only has an "internal" hydrogen-hydrogen interaction when in the s-cis conformation, therefore it should react about as fast as 1,3-butadiene - in between the extreme rates of the other two compounds.