I know other's likely have already stated some of these, but for what it's worth.
1) There is no such thing as buying too much packing tape.
2) There is no such thing as too many boxes
3) There is no such thing as being "too specific" when labling contents of boxes.
Figure out what you want to actually take with you. Toss, donate, or sell things that you just don't want or aren't worth the hassle of moving. Tip: If it's still in a box from your last move...get rid of it!
Start with items you don't use much or won't miss until the move. All knick-knacks, out of season clothes, bedding and towels not needed until the move, books, and I'd say even a fair amount of toys. Tip: when box is half full, pick it up and see how heavy it is. If it is too heavy at half-full, take the stuff out and use a smaller box, or fill up the rest of the space with a really light item, like a lamp shade or a pillow. For books, cd's, and dvd's, use the smallest boxes you can, they get heavy fast. Another tip: Trash bags work great for cloths, towels, bedding, and stuffed animals! You can lable them with printer lables.
If you're only a few weeks away from moving, I'd start packing up the kitchen too, and use paper products as needed once the dishes/flatware are packed. Just leave the pots/pans and a few bits of bakeware for the very end so you can still cook.
Book your moving van early, especially if you are moving at the end of May, you'll be competing with a lot of college students and plus regular people moving at the end of their monthly lease. U-Haul has a sister site that helps you find people to help load/unload your moving van if you don't have enough friends/family that are able to help you. And if you can afford it, save yourself a lot of work and hire a cleaning crew to clean your house once it's packed. Some things are just worth the money! If do clean yourself, save some money and use straight white vinager and reusable wash cloths to do windows, and half water/vinager to wash most other surfaces. It gets just as clean for a fraction of the cost of Windex, 409, and paper towels!