Another vote for Godalming - though I'm biased because I live there already. Commute in to London is fine - train is quick and comfortable and you always get a seat. I loved communting as you get a quiet 45 mins at start/end of day with book and coffee! I get the train in to Guildford for work now, which only takes a few minutes.
Primary schools are mostly good. Taten, Moss Lane and Busbridge are the two most popular, St Edmunds if you're Catholic. There are lots of good village schools near as well - Milford, Witley, Shackleford, Puttenham. School entry is quite competitive though so you need to check distances quite carefully on the Surry website. It's also split infant/junior, so also look at distances to junior schools. The Aarons Hill area and Green Oaks/Loseley Fields schools are the ones that some people avoid.
It's a really friendly place to live - loads of people with young children so a big community around nurseries (high demand for places though), schools and the local mummy-cafe/baby groups/NCT etc. It's lovely if you like somewhere you'll always bump in to someone you know to have coffee with/at the park/supermarket.
JooLoo, your budget should get you something nice - depending on your happy distance for walking to station - I'd look at Busbridge. Some of the bottom end of Farncombe is lovely, the Godalming side of the railway line.
Nice houses do move really quickly though - we're hoping to exchange next week/complete September on something and put in an asking price offer within two days of it going on the market to secure it. We sold ours (much cheaper cottage) within 10 days for pretty much asking price.
Sorry for essay - hope it's helpful!