MY DH is a retired Marine, so we have the packing thing down, lol...
I never used boxes for our dressered clothes (the ones we didn't need for travel, that is)- we would load the drawer-less dressers on the truck, then bring in the drawers full of clothes and put them in, and wrap with moving blankets.
We also filled tv cabinets and the like with our clothes, once the cabinet was empty of the tv/stereo/wine and on the truck- open the doors, put everything in neatly, and wrap it shut with that movers shrink wrap. Which brings to mind- fill every drawer, shelf/cubby of all your furniture. For drawers, you can fill those then carry to the truck most times. But big things like cubbies or tv cabinets, fill those after you get it on the truck so as to not have too much weight when carrying- that is a good place for spare blankets!
We never used good blankets to protect furniture, as the straps wear heavily on everything, as evidenced by the holes left in them- wouldn't want that to happen to a good blanket. Yes, use them inside boxes or whatnot, just not on actual furniture with strapping. (But then we always had long distance moves. Local moves, blankets probably aren't bad for that use).
Be careful of random things digging into appliances or furniture when it is on the truck- our fridge has a few digs in the paint b/c the foot of something rubbed on it, where the blanket didn't go all the way down. It is amazing how much things shimmy no matter how tightly you think you have it packed.
I used all manners of towel and clothing to wrap dishes- is easier and less wasteful. oh, and once we switched to Correlle, those were so much easier to pack, lol.
I never went room by room, as you ended up with too many boxes then. Pack physically like with like, as long as you don't overload, and then use the clothing or soft things like throw blankets, stufties, towels, etc. to pad the box. By like with like, I mean in accordance to the rules of Tetris, lol- whatever fits on/with something else in the box, without breaking things obviously. This makes for many less boxes!
Buy/use lots of straps, as you can use them to hang things from the roof of some moving trucks. Speaking of- before you rent it- be sure the truck has lots of tie down points.
Those tie down points are *extremely* useful to lock in sections. So that as you go along packing the truck, things get locked in like Tetris, then you start filling again.
We never cared where our beds, bedding, clothing beyond what was for travelling ended up. 99% of the time we got the entire 26ft or two 16ft long P.O.D.S. units fully unloaded the day we/it/them got there. And that was at times after driving for the entire length of the country, and with only 2 adults and semi-useful child lol. And even if you don't get it all unloaded- that is what the air mattress/sleeping bag in the trunk was for.
Heck, our last move, the retirement one, we went from coastal SC to near Spokane, WA. DH drove the truck, I drove my car. We had the ENTIRE 26 ft moving truck loaded to the gills... get it closed, look out at it... the dang thing is leaning so far on one tire it is nearly to the ground!! It had a bad axle. We had to unload it and reload it all onto a new truck!!! Did all that in one day again, in the rain, and were only behind by a day at that point.
Which reminds me of another point---- if you are towing a car- DO NOT take their word for it that the dolley will work!! Try it days before! We had to pay $1200 extra last minute to ship DH's car! Which in retrospect might have been a Godsend, as the replacement truck they gave us had absolutely no power. Another point- maybe stay away from Budget for long hauls- we were not happy with that whole fiasco of the broken truck and non-fitting car dolley. And they only refunded us $400 after the massive inconveniences of unloading and reloading and shipping his car.
Okay, that was a lot of info. Hope it all helps.

And good luck!