I'm no expert, but let me get the ball rolling. Before the construction of the First Transcontinental Railroad in the 1860s, you would have had to make at least some portion of the trip by covered wagon, likely along the Oregon Trail. According to The Emigrant's Guide to Oregon and California (first published in 1845), the typical family would have traveled with one or two wagons, a team of oxen, firearms (pistols and rifles), several hundred pounds of food, cooking utensils, baggage and sundry other items.

This site lists the likely cost of all the supplies as between $800 and $1200: http://www.bankrate.com/brm/news/moving_on/2004_guide/oregon-sideone.asp

(See also: http://www.oregontrailcenter.org/HistoricalTrails/Supplies.htm)

Now, as for the cost of the train from New York to San Francisco in June 1870, Stephen Ambrose cites the following rates in his book Nothing Like It in the World (p. 369): $136 for first class in a Pullman sleeping car, $110 for second class, $65 for third or "emigrant" class seats on a bench.

Again, I'm no expert: please correct me if I got anything wrong here.

The ceremonial golden spike connecting the union pacific and central Pacific railroads was hammered in in 1869 . So anything before that could not be 100% rail.(Assuming mid 1800s as 1850s). For a couple of years after the golden spike was struck, passengers would still have to disembark and make certain portions of the trip off rail, eg cross the San Joaquin river or the Missouri river by boat (until bridges were built). Is you still couldn't go coast to coast.

I will wait for the flaired users to suggest cost or alternate routes or similar info

Edit: a bit more on the transcontinental railroad. You could take the stagecoach over land till the Missouri river. Or you could go by ship around.

In 1876 an express train left new York city and reached San Francisco in just over 83 hours (3.5 days) later. Your link talks about the direct route taking 4 days now...