To be quite honest, I haven't read very much about the journey from China to California itself, and I actually wouldn't be surprised if there were no surviving primary sources from those that took the voyage (there often aren't for issues of early Chinese immigrants). I can attest that it was nothing like the absolutely putrid conditions of the triangle trade in the Atlantic. Many Chinese purchased their own tickets over to the U.S., though lots also used a credit-ticket system.

While I don't have any sources for what the journey was like during the gold rush era, I do have some that would indicate what the journey was like from 1910-1940, as many Chinese left poems carved into the walls of the Angel Island Immigration Station, which was operating for those years.

The sea-scape resembles lichen twisting and turning for a thousand li.
There is no shore to land and it is difficult to walk
With a gentle breeze I arrived at the city thinking all would be so
At ease, how was one to know he was to live in a wooden building?

.

Everyone says travelling to North America is a pleasure
I suffered misery on the ship and sadness in the wooden building
After several interrogations, still I am not done
I sigh because my compatriots are being forcibly detained 

.

Originally, I had intended to come to America last year
Lack of money delayed me until early autumn
It was on the day that the Weaver Maiden met the Cowherd
That I took Passage on the President Lincoln
I ate wind and tasted waves for more than twenty days
Fortunately, I arrived safely on the American continent
I thought I could land in a few days
How was I to know I would become a prisoner suffering in the wooden building?
The barbarians' abuse is really difficult to take
When my family's circumstances stir my emotions, a double stream of tears flow
I only wish I can land in San Francisco soon,
Thus sparing me this additional sorrow here

My impression from the poems is that while the voyage may not have been particularly enjoyable, it wasn't necessarily squalid either. Certainly, the immigrants found the immigration station far less agreeable than the ship.

Let's go back to the gold rush era.

There were a few different motivations for leaving. You are correct in thinking that the primary one was economic. Almost all Chinese immigrants to the U.S. came from the Pearl River Delta region, which was not doing great economically at the time. For some immigrants, their only alternative to leaving China was starvation. This was compounded by exaggerated stories of how rich one might become by moving to "Gold Mountain" (the Chinese term for California), which was even further exacerbated by shady ship owners trying to sell additional tickets by promising riches to any who would embark with him.

The stories weren't totally incorrect--there was a liveable wage to be made in California, but many Chinese weren't able to accumulate the wealth to return to China, which had originally been the plan. Many, though, were able to send home remittances--about an average of $30/year.

One other push factor in the delta was from triad members who were worried about being punished for participation in the Taiping Rebellion, though this was a secondary factor to economics.

There were some who were forcibly brought to the U.S. The immigration wave to California, however, happened in the midst of a greater Chinese diaspora that send Chinese "coolie" labour all around the world, including Central America, southeast Asia, and parts of Oceania. Because many of these locations were far less enticing than California, many more Chinese laborers that had been forcibly removed from China were sent there, rather than California, which had an ample amount of voluntary immigrants already.

Information on the push/pull factors of immigration are from June Mei's "Origins of Emigration: Guangdong to California, 1850-1882," published in Modern China Vol. 5, No. 4.

Poems are taken from "Island: Poetry and History of Chinese Immigrants on Angel Island, 1910-1940"