Gray tin, also known as $alpha$-Sn, can be turned into a three-dimensional topological insulator (3D-TI) by strain and finite size effects. Such room temperature 3D-TI is peculiarly interesting for spintronics due to the spin-momentum locking along the Dirac cone (linear dispersion) of the surface states. Angle resolved photoemission spectroscopy (ARPES) has been used to investigate the dispersion close to the Fermi level in thin (0,0,1)-oriented epitaxially strained films of $alpha$-Sn, for different film thicknesses as well as for different capping layers (Al, AlO$_x$ and MgO). Indeed a proper capping layer is necessary to be able to use $alpha$-Sn surface states for spintronics applications. In contrast with free surfaces or surfaces coated with Ag, coating the $alpha$-Sn surface with Al or AlO$_x$ leads to a drop of the Fermi level below the Dirac point, an important consequence for transport is the presence of bulk states at the Fermi level. $alpha$-Sn films coated by AlO$_x$ are studied by electrical magnetotransport: despite clear evidence of surface states revealed by Shubnikov-de Haas oscillations, an important part of the magneto-transport properties is governed by bulk electronic states attributed to the $Gamma 8$ band, as suggested by {it ab-initio} calculations.