Hi I came here from Leicester 7years ago and have found it a really nice place to live.
Like you I wasn't sure where to move and also like you I had a young family.
Hillier and Wilson estate agents tend to have some of the better property (not sure why?) we've move 3 times and found them really helpful.

From my experience on the edge of Newbury (in the £350-£400K bracket):
Knightbridge Road and Salcombe Road (going out towards Enbourne); as well as
Gloucester Road, Craven Road (closer to town)
are all very family friendly places to live, close enough to the town centre but also very close to the canal and fields for nice walks all in the areas of good schools.
Wash Common is nice but a bit too far out of town

Out of Newbury

The best state funded primary school (2010) is in the village of Hermitage

Thatcham is notoriously rough and the kids are a bit chavy, so my advice would be to steer clear of there!

Good luck.