What should i bring on my truck?

First off DO NOT USE A PROPANE HEATER of any kind in your truck. The fumes are deadly in an enclosed area.
If you want to run appliances buy an inverter and have it installed directly to the batteries. A 1500 watt to 2500 watt will run anything you want on a truck; Microwaves, tv's, dvd players, video games, toaster ovens, laptop computers, cell phones, crock pots, coolers or refrigerators, sandwich makers, and coffee pots are common appliances on otr trucks today. Small portable toilets are also handy but will stink up the sleeper pretty quick and with all this gear on board you wont have much space to get around nor have given your partner much room for his/her gear.

Keep it simple for just starting out;
Bring pens, notebooks, a ruler, a calculator, and a binder for your paperwork.
Bring a bedroll with a pillow.
Bring 2 weeks worth of under clothes and at least a weeks worth of work clothes.
2 jackets would be smart. 1 that is rainproof and 1 that will keep you warm in colder climes.
2 pairs of shoes would be a good idea in case you get 1 pair wet or muddy you will be able to switch.
2 pairs of gloves. 1 work pair and 1 rubber coated pair for fueling the truck.
Personal hygiene kit with shampoo, soap, deodorant, nail clippers, tweezers, razor and blades, shaving soap, dental floss, toothbrush and toothpaste and anti fungal spray or powder (for athletes foot from using public showers).
Basic over the counter drugs like advil, immodium ad, neosporin, dayquil, vitamin c drops (will help sustain your immune system), gold bond powder (or something with cornstarch for sweaty nether regions), pepcid ac etc.
A basic tool kit with a flashlight, pliers, vice grips, screw drivers, hammer and wrenches will come in handy as will a roll of duct tape, spare fuses, and bulbs for the truck, a truck tire guage and 50 foot air line with tire chuck and glad hand adapter.

 

I forgot to mention you should get a laminated motor carriers atlas. This will have a list of restricted routes and low underpasses as well as mileages from major cities. It is a necessity out here.

Inverters are very easy to install yourself. If you are unsure you are capable then by all means ask someone in the company shop to install it correctly for you.
As for a portable stove I would recommend something like a sandwich maker or george foreman type grill with removable plates for cleaning. As for something like a hot plate I suppose its possible but I wouldnt recommend trying to use it while the truck is moving.