If you have any bike shops near you,find out if they are good. This means that they explain things to newbies such as yourself and are willing to take time to find you the right bikes. Ideally, they should find out about the circumstances in which you ride as a family, should be familiar with the trails you use and show why any bikes they suggest fit your particular needs.
If they are impatient because you're not knowledgeable or because you're a woman (not unkown, alas), find another one.
As for bikes, especially for growing youngsters, try not to get ones they'll "grow into". If they're too big at the start, they won't enjoy riding as much as they otherwise would. One indication that the latter's the case is that they can only just touch the ground with the saddle right down and the handlebars are well above sadddle height. Such bikes also tend to be too long, leading to the riders having to stretch to reach the bars - which ain't good for young backs, let alone easy bike control.
It's not my budget, so I can't give specific answers, particularly from the UK. However, a UK brand which is universally regarded as the best value and best child-design centred has now opened a US mail order branch in Portland. they may be more than you are prepared to spend, but I can say that, from UK experience, they hold their value extraordinarily well**, so the net annual cost is less than it seems.
Their webiste is http://www.islabikes.com/us/how_to_buy.html
and contains usefull info on how to size up the most suitable model.
There is a useful US published book called Bicycling with Children by Trudy Bell - www.mountaineersbooks.org
for details if it's still in print.
** If you have time to do the research, check prices on Ebay and Craigslist and compare them with the cost of the models listed when new. That will give you a good idea of their quality.
Finally, can you find out if there are any other cycling families near you? A good bike shop should be able to help, either from knowing them directly, or by putting an ad in their window.
Good luck and welcome to our world.