Go with a sleeping bag, because you will be hot bunking on the lower berth when moving. Forget sheets until you're in your own truck. Don't forget a pillow.
Shower clogs!!! Unless you enjoy athletes foot.
Go long on underwear and socks, not so much on outer wear. Leave anything in light colors at home - lithium grease stains don't come out.
Don't forget something warmer to wear, gloves, warm hat. It may be nice now, but it's already snowing at higher elevations.
Storage space is really limited in trucks, so what can't be got into your limited cabinet space, you'll be sleeping with on the top bunk when the truck isn't moving.
Personal electronics - a smart phone and charger can be used for most online tasks. WiFi coverage ain't the best, so I usually recommend you get a good national coverage plan - with a serious network to support it.
Bank account that has online banking services! You need to get your settlements on direct deposit to a bank account to avoid paying huge ATM charges, Western Union fees, etc. Getting it sent to your home in a check means you won't have access to your money. I put $150 on the personal account side of my fuel card, and get the rest on direct deposit. Having some cash on hand is necessary to pay for cash tolls, scale tickets, and coffee money.
Most of your bills can be dealt with online, which is really convenient. If you have to mail something, make sure you have stamps. Many truck stops don't csrry them any longer.