Most of the expeditions if the age of exploration were privately funded. Portuguese traders in Africa and Spanish conquistadors were almost entirely self-financed. Even Colombus was mostly privately financed. Most early modern monarchs had almost no money to fund standing armys or navys. In this period, monarchs tended to reward explorers, merchants, conquerors with special social or economic privileges.

For some good books, old and new on this you can see

Restall, Seven Myths of the Spanish Conquest (especially the myth of the King's army)

J.H. Parry Age of Reconnaissance and Spanish Seaborn Empire

Carl Sauer, Early Spanish Main

Lockhart and Schwartz, Early Latin America