Just to add to what was said here, Crockett most likely left a "fancy" percussion rifle behind because there were no sources of percussion caps in Texas at the time. To give you an idea of the timeframe, Colt patented his revolver before the Alamo fell. Took years to get to Texas in the form of a purchase by the Texian Navy. These revolvers found their way into the hands of the Texas Rangers after Sam Houston disbanded the Navy a few years later.
The .36 caliber was fairly typical of the rifles used by Texians in the war for Texas Independence... "squirrel" rifles were much more common than any large caliber weapon. Texas was mostly settled by men from Tennessee, Missouri, Louisiana and Alabama, and many of them had rifles for shooting small game vs. large game.
The book Texian Illiad actually references the weapons used in the revolution quite thoroughly for a general history book, with numerous extremely detailed illustrations and a nice sequence of the loading of a brown bess musket used by the Mexicans. They had a great deal of napoleonic-era British surplus, including squads with Baker rifles that were very capable. The Texians used whatever weapons they had, which were mainly small game rifles and a few muskets and shotguns. There are several accounts where Texians dumped the horrible mexican powder out of paper cartridges and melted down the balls to fit their smaller rifles. The Texians had a decided advantage with the use of DuPont powder over the Mexicans, which had to double-charge their muskets with sorry powder of their own manufacture.