Fill up in Tulare, or there abouts. You may not need gas, but from near Bakersfield to Barstow, gas is expensive, and stations can be miles apart.
If you come in to Barstow on 58, get on I-15 north to I-40 to Kingman, you won’t see an exit to get gas. From 58, take I-15 south about a mile. There you will find stations aplenty, and about the cheapest until you get to Kingman.
While on 58, you will pass the Tehachapi loop (if you’re a railroad buff) and on up to Tehachapi. It’s a steep grade, but don’t let it scare you. In Tehachapi is a fairly good BBQ place, The Red Door, if you’re in the mood for lunch. If you want to wait until Barstow, look for Peggy Sue’s - the food is OK, but the decor is fun.
If you want to call ahead for a hotel, stay at the Quality Inn in Kingman and ask for the ‘Martin Milner’ room, as in ‘Martin Milner slept here’. You may remember him from the old TV shows ‘Route 66’ and ‘Adam-12’, as well as a coupla times on ‘Dragnet’. It’s a basic hotel, but it’s clean, and has a fairly good free breakfast. If you want to splurge on a room, you can book the Andy Devine suite - he slept there too. It’s not much of a suite, really just an over-sized room. If you’re there for dinner, there’s a good BBQ place in town, but I can’t remember the name - ask the desk clerk.
I’ve been to Deming once some years ago, and I don’t remember it being much of a place. Consider driving a bit further to Las Cruces.
Otherwise, not much to add. When I go coast to coast, I have a choice of I-70/I-80 or I-40. I like I-40, because the food is better (BBQ and Tex-Mex, and onion burgers in Oklahoma), but I-70/I-80 is about 150 miles shorter, and has long stretches of 80 MPH in Wyoming and Utah. My I-40 travels is how I know the Bakersfield to Kingman route.
In fact, I depart Friday for the far coast. But I’m going east to west, so I’ll wave if we pass.