M.R.
Most people think this is frivolous, but for me it is, was, and will always be an absolute must - can you afford to hire movers? I have used them for my past 2 moves and will NEVER move my house on my own again! My stress level was significantly reduced and I didn't feel physically exhausted. This was BC - before children! I cannot imagine chasing two toddlers around with doors constantly open and trying to move furniture and boxes.
I know money is definitely tight when buying a new house, especially with closing costs and such but if you are in a position to hire movers I highly recommend it.
To help your kids with packing (and for you to easily identify their boxes) let them pick out sheets of stickers. For example, the 3 year old gets Thomas the Train stickers and the 5 year old gets Hot Wheels (or whatever they may like) and let them put a sticker on each of their boxes. It might even encourage them to help with packing - "When you help mommy finish packing a box, you get a sticker for the box and a treat for you!"