The best boxes are bleach and detergent boxes, poached from your friendly, neighborhood grocery store. Egg boxes are rather durable, too, if you can get your hands on them. Banana boxes have nice handles, but the bottom is only covered with a thick piece of paper.
Regarding dresser drawers-- take the drawers out (makes dresser lighter!) but don't worry about removing the items. Just move them as is.
Friends and family are usually bribable. I can usually lure my family with pizza. And since we're moving, I don't have to worry about making conversation with them.
Keep like items together-- or at least like rooms. Kitchen stuff with kitchen stuff, etc. Probably best to keep the IMPORTANT things that you know you'll need quickly (personal hygiene, medications, etc.) with you, same as you would with traveling.
Try to plan your move so you're not tripping over boxes while moving furniture. Plastic baggies work great for containing loosable items like pens and other small things. Start packing things you don't use early so you have as much ready as possible come moving day.
I've only moved twice (not counting moving from my summer bedroom to my winter one.) Aside from generic advice, I've concluded that I will, for the next and all subsequent moves until I die, only make one trip. I will rent a truck, load everything into said truck and move. Last time we moved, we decided we could do it just using the fleet of cars and pick-up truck. That was a lot of time hauling back and forth across the county that was just agitating. I'd rather load it up, drive over, unload it all, then set about unpacking.
I'm one of those folks who prefers to get everything put into it's place and set up nicely. This works rather well with Hubby since he doesn't tolerate change well-- if everything is put away, he can adjust faster since there's less transition. No boxes hanging out everywhere!
Moving is a good time to ditch old things you don't want, but at the same time, don't be a jerk about them (filling apartment dumpsters beyond full is one example another is just leaving your crap in the house you're leaving.) Moving is also a good time marker for seeing if you need to keep things-- when Hubby and I moved out of our little apartment, we noted that there were quite a few things that stayed in storage the entire five years without even a thought of retrieval. Somethings, like books, were there because they had not place to go in the apt, but others were things that clearly were no longer used (like clothes that hadn't been worn in five years.)
If you have a lots of helpers, figure out roles for them to do that don't include wandering around useless. Someone can wrap dishes in newspaper, someone can box up books, etc. I like to play dictator, so I spend a lot of time seeing what folks are up to. =)