For the drive, after you get off the left coast you can plan your route to carry you pretty much all the way through Constitutional Carry states. Idaho, Montana, Wyoming, South Dakota, Iowa, Missouri, Indiana, Kentucky, Ohio, West Virginia. Only states you can't along the way, depending on your route, are Illinois, Pennsylvania, Maryland, and Virginia. Virginia and Pennsylvania, if you have a concealed carry whatever your state calls it, is likely reciprocal.
Please, do your additional research and make sure you're good for carry in all those states.
For Illinois and Maryland, they have proven in the past to be very aggressive against gun owners from out of state. Above mention about taking it apart, locking it in a box, locking that box in a box, is good advice and exactly what I've done in the past. I make sure I fuel up at the Iowa and Indiana state lines and I don't stop for shit in Illinois, making sure to leave nothing but exhaust fumes. Sure would be nice if my folks moved to this side of the Mississippi, as visiting them is the only thing that gets me to cross Old Muddy into Obamaland.
When my ex moved my kids to eastern shore Maryland, I moved to coastal Virginia because I refused to live in that commie state. I met her more often than not of the Virginia side of the state line to hand them off. For you temporarily living there, I recommend you keep the gun at your temporary home for personal defense there and do not travel with it until you leave the state.
As for if you (or any other travelers reading this) need a firearm on the trip? Abso-fucking-lutely. Shady shit happens at truck stops and rest areas, from aggressive doped up pan handlers to car jackings and armed robberies, and how nice your hotel is
has virtually nothing to do with how safe you are. Not knowing the territory and neighborhoods is bad enough, nobody wants to be Clark Griswold pulling off the
wrong exit in East St. Louis, but that's a real threat. Being at an interstate exit is also a heightened threat due to the easy avenue of escape for the criminals along with ease of blending into the transient environment, and they know it. Out of state plates only heighten that risk because they expect you to be unarmed, especially with left coast plates. They're dumbass criminals, but they're not stupid.
As for what gun to carry, the permanent answer is always the gun you know best and will actually carry at all times. Getting out to pump gas, carry. Going into the pisser for 30 seconds? Carry. Stretching the legs for just a moment? Carry.