We will be moving from Asia (Singapore) to St Albans too shortly
But we've explored the area thoroughly since we have friends and relatives living in Herts and make trips to the area each time we visit the UK.
A really fam fab place filled with shops (Marks & Spencer, and lovely restaurants/cafes/pubs (it has the oldest pub in England I believe) and it is so easy to get into London. Great recreational facilities and parks. A real commuter's dream (25 mins into Kings X).
Schools are generally good - check out Ofsted for reports on insights into schools and also Rightmove - a property site - they have a school checker with Ofsted ratings (outstanding, good, requires improvement). There is also a FB group for more insider info.
At 3, your child will qualify for 15 hours free nursery - but you might have to look at private options as the state nurseries are probably full since applications closed in Jan/Feb.
We've heard that Wainscot Nursery and Mount Carmel are great for little ones and will be checking them out when we get there in June.
Your seven year old should be in Year 2 or Year 3 (school year starts in Sept) depending on when she was born.
For your budget you should be able to find a decent property in St Albans.
But do move fast. Good properties near good schools get snapped up pretty quickly. Unlike the rest of the UK, we found that there is a more formal rental application process with lots of documents required (we tried to move to St Albans a few years back but my hubby was posted to Switzerland instead).