Welcome from the former colonies. Glad you are here.
The Sussex, Australorp, and Orpington are larger breeds, suitable for eggs and meat, but they cost a little more to feed than the smaller egg-laying breeds. They should be readily available in the UK. The only Sussex readily available in the States is the Speckled. These three breeds are reputed to have docile, mellow personalities. I'm not familiar with many of the breeds your countrymen mentioned other than the black rock, which is really a mix and I'd also consider a good choice. With the black rock, you know if you are getting male or female. With the other breeds, you may wind up with unwanted roosters.
You might look into what breeds or mixes the egg producers in the UK raise. Those will be the most efficient egglayers.
As far as age, you do want young birds. With young children, you may want them to see the birds grow from babies. It will not take that long for them to grow up and it can be quite an experience. It is easier to train chickens to be handled if you start young, but you can tame older birds. Just more work. If you are planning on eating them after their productive egg laying days are over, that could cause some difficulties with young children. You know your children and your goals, so your choice.
Point of lay pullets could be another good choice but a little more expensive. People want to recover cost of food, get some return on taking the risk of mortality, and get a little money for their time and effort. These are pullets about 16 to 20 weeks old and will begin laying in a month or two. Some advantages are that you know they are pullets, not roosters, and you don't need the brooder facilities.
It can vary quite a bit by individual chicken, but generally chickens produce eggs most efficiently during their first two years of life. Then, after each molt, egg production drops about 15% each year. You might want to consider this if eggs are your primary goal.
Good Luck!!