The price vairies nationally and by the amount of stuff/size of house so I think you are best to do a bit of shopping around for an idea of the cost.
First off I would be as ruthless as you can and sell/donate/tip anything you can.
Then I would start by clearing the garage or loft out so you have an empty storage space. Box up the things you don't need first - like the contents of the garage and loft. Label all boxes on all sides and number and name them. e.g garage box 1, then write and inventory of the boxes. So box 1 might have tools and paint brushes.
Dismantle anything like garden swings and bbq and store ready for transport.
Then start in the house, pack up books and ornaments, pictures, curtains and cushions, anything that you don't need to use.
Make a start with the DC's toys most can be packed early.
Then go through each room one at a time.
Don't forget to leave kettle, cups, tea etc in the last box and keep it to hand. You will need cleaning materials to hand too so you can give your house a quick clean before you leave and the new house when you get there.
If you can dispatch your DC to someone on moving day that will be a big help.
Get the DC to pack their own moving box with the things they will need on the first night, so pjs and clean clothes for the morning, toiletries, book for bed, dvd and a few toys. That will get them involved and they can look forward to upacking their own special box when they get there. Hopefully it will stop them wanting XYZ that is deeply burried!!
The main thing is to be organised with the boxes and knowing which room each box needs to go in, and roughly what is in each box.
I find copious amounts of gin to help too.....but you are probably best off leaving it untill you arrive 