Kaluza Klein is not a cosmological model per se -- it's an attempt at unifying the gravitational and electromagnetic force using extra dimensions.
Braneworld cosmology is a rather large area: Steinhardt and Turok's cyclic model is based on braneworlds -- in fact, it's an extension on the Ekpyrotic Universe. There are several other kinds of 'bouncing' or 'oscillating' universe models -- some based on branes some not. The Pre Big Bang model of Gasperini and Veniziano is a string theory-inspired bounce model. But these are not inflation models.
There are string/brane gas models, in which the early universe is postulated to have passed through a thermodynamic string/brane gas phase. Early developments are in papers by Tseytlin & Vafa and Brandenberger & Vafa.
Inflation is another general class of early universe theories. There are several different classes of inflation models, but perhaps the broadest distinction can be made between 'eternal' and non-eternal inflation.
