I would recommend that you go buy boxes. they will be sturdier, easier to move, protect stuff inside better. I woud defintely recommend getting wardrobe boxes with the hanging bar, this way yoiu can just take clothes out of your closet and hang them directly and not go through the effort of taking them off hangers and putting them in bags etc and then putting them back on hangers.
if you dont want to shell out money for watdrobe boxes I would recomment that you tie hangers with a cord and then another cord around the clothes, make clusters of 12 or so, more will be too tough to carry and things will also start slipping and falling.
stuff that is not breakable, toys and stuff, just toss them into boxes, no use with the hassle of doing packing box tetris for those. you may need a few extra boxes but well worth the time saved.
and yes, take the opportunity to purge old unneeded stuff, wrong sizes, stuff you dont wear or use etc. less stuff to move plus the new place will start with a clean slate.
for dishes get dish boxes, and wrap each item in paper..get the clean packing paper, newspapers may work too, but sometimes their ink would just get on everything and you will be stuck with having to wash all dishes once u unpack.
Great tips X2. I'd go with hanger and cord because it's cheap.