I have just returned from a C to C tour which included part of the Western Express (riding east to west).
As Ben posts, motel/hotel accommodation in Eureka and Austin was a bit scarce. The motel I stayed at in Eureka, filled up prety quickly & I was lucky to get the last available room in Austin, where I got snowed in (late May). I had to camp at Cold Springs Station, although I might have been able to get a room at Middlegate Station had I cycled further that day, but then perhpas not.
Baker is only a small place, with a restaurant which is not open every day of the week, and a grocery store that looks like it has come out of Cold War Europe. Don't rely on stocking up there. The motel where I stayed in Baker seemed to fill up quickly, once they opened for registrations (3.30pm) and the diner that was attached wasn't open that particular night, (no chef). Milford UT, also has limited motel accommodation although the motel you will come across on the western edge of town is a great place to stay, and has a diner attached to it.
US50 between Fallon and sand Mountain was particularly harrowing. I rode it on Memorial Monday, and there was a very large volume of RV traffic coming away from some ATV event at Sand Mountain. I would advise doing some research on the internet about what events have been scheduled for Sand Mountain, and to avoid it on week-ends if at all possible.
As Ben also posted, the grades of the climbs through Nevada are all manageable. It is the wind which is the killer.
Notwithstanding all that, the W.E. experience was stunningly beautiful, and I wouldn't hesitate to recommend it to anyone.
Please feel free to ask me for any further details if you think I can help.
Hope you have a safe and enjoyable ride.