We've camped at Furnace Creek twice, and did want reservations, because we didn't want to drive all the way down from BC only to find No Room at the Inn. Sometimes during our stay they were full, sometimes not. Apparently they are liable to fill up with Californians on long weekends, and also if there are certain special events going on in the area. About 10 of the Park Service sites have hookups, the rest are boondocking.
The concession lodge at Furnace Creek also has some RV sites, with hookups. But more expensive.
One nice thing about Furnace Creek is that $5 will buy you a swim in the lodge's warm springs pool, including showers in the change rooms.
There is overflow camping across the highway at the Sunset CG, but it's not so inviting: Furnace Creek has shade trees, but Sunset looks like a big gravel parking lot. Texas Springs is nearby, but they don't allow generators and I don't think the sites are very long.
We'll be back down that way in Feb/March and will stay at the Shoshone RV park in Shoshone, CA, making a few day trips into DVNP. Shoshone is a bit down-at-the-heels, but we wanted full hookups for a longer stay, and do not like the big RV parks where you're wedged in between the motorhomes and 5th wheel slide-outs. There are hiking trails in the vicinity, a big library, and a smaller on-site warm springs swimming pool.
We will probably take I-84 through eastern Washington & Oregon, and then pick up I-15 at Tremonton, UT to get there. It's not the most direct route, but in the winter, we look for low passes and places to hole up off the highway if the weather turns bad. We have people to visit in SLC. Nevada is probably going to be drier than the Wasatch Front, but if there is a blizzard, the route through Jackpot and Wells, NV has some very long, lonely stretches of road with no real place to get off the highway.