The mono-, di-, and tetrahydrates of trifluoromethanesulfonic acid, which contain characteristic H3O+, H5O2+, and H9O4+ structures, provide model systems for understanding proton transport in materials with high perfluorosulfonic acid density such as perfluorosulfonic acid membranes commonly employed in hydrogen fuel cells. Ab initio molecular dynamics simulations indicate that protons in these solids are predisposed to transfer to the water most strongly bound to sulfonate groups via a grotthuss-type mechanism, but quickly return to the most solvated defect structure either due to the lack of a nearby species to stabilize the new defect or a preference for the proton to be maximally hydrated. Path integral molecular dynamics of the mono- and dihydrate reveal significant quantum effects that facilitate proton transfer to the "presolvated" water or SO3- in the first solvation shell and increase the Zundel character of all the defects. These trends are quantified in free energy profiles for each bonding environment. Hydrogen bonding criteria for HOH-OH2 and HOH-O3S are extracted from the two-dimensional potential of mean force. The quantum radial distribution function, radius of gyration, and root-mean-square displacement position correlation function show that the protonic charge is distributed over two or more water molecules. Metastable structural defects with one excess proton shared between two sulfonate groups and another Zundel or Eigen type cation defect are found for the mono- and dihydrate but not for the tetrahydrate crystal. Results for the tetrahydrate native crystal exhibit minor differences at 210 and 250 K. IR spectra are calculated for all native and stable defect structures. Graph theory techniques ire used to characterize the chain lengths and ring sizes in the hydrogen bond network. Low conductivities when limited water is present may be attributable to trapping of protons between SO3- groups and the increased probability that protons transfer to waters bridging two different sulfonate groups.