Most depictions of Miners in the late 19th century show them handing small pieces of gold to a man behind a cage for what appears to be a small amount of money. What kind of exchange rate was there at this time? Did they shorthand the Miners by a large amount in regards to how much the gold was actually worth? Was the exchange different for company Miners and people with their own claims??
The exchange rate was about $16 per ounce and this was generally honored unless the gold was pale and apparently alloyed with a lesser metal (as was the case with gold from western Utah Territory, for example). California Gold Rush miners usually worked for themselves in small teams, so there wasn't a matter of "company miners" versus "people with their own claims": California miners typically worked their own claims.
Gold could be used for barter in the early communities, although very quickly various local mints started producing coinage to facilitate trade.
I'm writing notes for the Journals of Alfred Doten, a '49er (who wrote from 1849 to 1903), and I wrote the following on the question of minting gold:
In the wake of the California Gold Rush, which began in 1848/1849, there was a chronic shortage of coinage to meet the demand caused by the thousands of new arrivals and by the increase in commerce they created. Trading in gold nuggets and dust required constant weighing of the precious metal and it depended on an often-incorrect assumption about the purity of the metal. Various private coins were issued to fill this gap and the United States Assay Office of Gold in San Francisco also began issuing stamped bullion with value indicated to facilitate trade. Congress was slow to create a U.S. Mint in San Francisco, but after some delay, that authorization was passed in 1853. At that point, the U.S. Assay Office closed, but there was a gap in operation as the U.S. Mint did not open until April 3, 1854, and even then, it was not ready to launch into production. John Glover Kellogg was a '49er who had secured employment with the U.S. Assay Office, and so he understood the process of coinage. To address the demand for reliable coinage in the thriving economy of the West, Kellogg with a series of partners began issuing twenty dollar "double eagle" gold coins beginning in early 1854, boasting that he was capable of a daily production of one thousand gold coins worth $20,000 per day. After the U.S. Mint formally opened, the need for coinage was far from being satisfied by the federal government, because copper and certain acids needed in the coinage process were in short supply. Kellogg consequently continued to produce his coins throughout 1854 and into 1855, ultimately minting about $6 million worth of the double eagle gold pieces. Doten is describing a devaluing of these privately issued coins in 1857; federally produced gold coins were becoming numerous enough that people were beginning to prefer official U.S. currency in place of private coins, resulting in a reduced value of the latter.
Source: Donald H. Kagin, Private Gold Coins and Patterns of the United States (New York: Arco Publishing, 1981).
'49ers hoped to make their "pile" - which most regarded as something in the order of $10k so they could return home and go into business or buy a profitable farm. Becoming a millionaire was well outside the imagination of miners of the "extensive" gold resource. Later underground "intensive" deposits of gold and silver allowed for one to imagine becoming a millionaire, but that was extremely rare.
A good day was when miners retrieved the equivalent of $3 or $4 worth of gold per day. Obviously, that was not to lead to gathering one's "pile," but it did mean survival until one found a truly rich claim, which was all too elusive for most.
FYI: The Doten diaries were published in 1979 with about half the words printed. I am volunteering to assist in the transcription of the entire 79 books, and I am the editor of the notes. Also co-edited The Gold Rush Letters of E. Allen Grosh and Hosea B. Grosh (2012) which informs this answer.