Best thing to do for the fish would be to get a large poly box or two from your local fish shop. Some give them for free, others charge around £2.50 each.
If the fish are non aggressive and small, and will be okay together for a period, simply fill the poly box with water and transport that way. Making sure it is clean first. When you get to your new house, get an air pump going in the box, leaving the lid on as much as you can.
You can also transport them in bags (from eBay or LFS) if you prefer or feel it is necessary. But keep them in the poly box for temperature and to keep them calmer in the dark.
Set up your tank again. Make sure this is the first thing you do for the sake of the fish.
Try and minimise the amount of time your filter is off, and always keep it wet as this helps.
You don't need to bring any additional water. Fill the tank up and bring it to temperature. Use warm water to make this process quicker, as long as the new house doesn't use a copper tank to warm water. Start filtration, pumps etc. You can then acclimatise the fish by placing small amounts of water in the poly box at regular intervals until conditions and temperature are brought more or less together. Alternatively, you can use bags to place the fish in your new set up and acclimatise that way, just like you would when you bring them home from the shop.
Unless it is a massive tank with obvious logistical issues, moving tanks isn't really a big issue if done right.