Early Texans, for the most part, didn't have no money for nothin'. That's not to say they were poor. As a group they were hard working and land rich, a combination that leads to growth in an agrarian economy.
But there was little gold or silver in the country, no ready medium of exchange. Some 'hammered dollars' still circulated. These were old Spanish silver dollars on which the face of the king had been beaten off after Mexico won her independence.
The first Texas currency - authorized by the Mexican government
Personal promissory notes and bills issued by banks in Southern states where used if both parties could agree they had value. The face value was discounted to a greater of lesser degree depending on the trust the receiving party had in the issuer. Many people where burned when notes turned out to be from defunct banks, and therefore worthless.
The treasury notes of the Republic were also little trusted, as the government had fallen in love with the printing press. Inflation is always a monetary phenomenon and Texans came to hate paper money.
They didn't trust banks either. In fact there was only one chartered bank in Texas before the Civil War, and it only existed because of a grandfather clause passed by the first congress. The Commercial and Agricultural Bank of Texas had received its charter from Mexico.
Merchants became de facto banks, accepting agricultural goods and issuing credit. Still, it was highly inefficient and a drag on the Texas economy.
The situation did not improve until the State and National Bank systems took firm root in the 1880s. Until then, any Texan would prefer to have a few coins jangling in his purse to a fat foll of bills in his pocket.