In 1860 you would have a few options.

The slowest overland route would be to hire a staff of guides and teamsters to guide your wagon train. Depending on time of year you’d either take the northern route through Salt Lake and then following the Humboldt River across northern Nevada. Total transit times could vary wildly based on travel conditions but 3 months would be typical. The northern route was faster, but because of the problems with mountain passes, especially through the Sierra Nevadas, it was only viable during the summer. You wanted to be done by October unless you maybe want to eat your friends.

The southern route was open year round. It followed the overland trail from Missouri down to Santa Fe, across to LA and then up the coast to San Fransisco. It would add another 600 miles and several weeks to your journey. Regardless of route, you have to add another 5 days or so for the train time from New York to Missouri.

By 1860 commercial service had opened up. The Butterfield Stagecoach Service was operating along the southern route. 596 hours of travel time, or 25 days. But the coaches only carried 9 passengers and very limited cargo so you’d have to reserve a lot of coaches, you wouldn’t exactly be traveling with your friends. But you could replicate the system, and travel in a train of coaches instead of wagons.

At best (no expense spared) you’re looking at at least a month of travel, and more likely something closer to 3 months.

But that’s only overland travel. You can also go by ship. In a lot of ways it’s a far more convenient way to travel, and with your crates it’s a lot more practical. Here again you have some options. For passengers and light goods the preferred option was to sail to Panama, portage across the isthmus and then board a new ship to sail up to San Francisco. This was a reasonably fast trip. As a lieutenant in 1852 Ulysses Grant made this trip in 43 days, even faster trips were possible, depending on weather.

Of course his unit crossed during a cholera outbreak. Out of 700 fellow travelers only 450 boarded the ship to San Fransisco. The rest were dead or at least recuperating from cholera and unable to continue with the unit. So your rich friends might not find that an acceptable risk just to get to San Fransisco faster. That said in 1855 the cross-Panama Railway had been built. So you’d likely only spend a few days in country not 18 like Grant had to do.

Panama also restricted heavy goods. The military had to send heavy stuff like artillery via the longer route around the tip of South America. Such journeys could take 5-6 months. And once the Railway was built, they became much rarer.

All told you’re looking at least a month sailing to and from Panama, or a month in coaches crossing the southwest deserts.

One option would be to take a steamer from San Francisco to Seattle, travel overland from there to Fort Benton on the Missouri River, take a paddle wheeler downriver to St Louis and finish the trip by train to New York.

.

39 hrs - San Francisco to Seattle -810 miles.

17 days - Seattle to Fort Benton - 680 miles

58 hrs - Fort Benton to St Louis - 1500 miles

48 hrs - St Louis to New York - 950 miles.

.

Rounding numbers up it would be concievable for a person to complete the water and rail portions of travel in 150 hours. Assumptions made are that the steamships have enough coal on board so that they don't have to stop for fuel, average speed is 19 knots and the Missouri River flows at 10 mph.

The distance from the coast to Fort Benton on the Missouri is a bit of a wild card but it should be conceivable that this party would be able to travel 40 miles per day by 1860.

So theoretically a person should be able to make the trip with a large party and supplies in around 27 days.