I commute from the Glossop area to the city centre. Unless you can leave at the crack of dawn, or well after rush hour, would not recommend driving in. However, the Glossop/Manchester train is good - quick, reasonably priced and generally reliable, although trains back go down to one/hour at night.
About an hour door to door including the drive to the station, but relatively stress free and worth it to live on the edge of the Peak District. Having endured hour commutes on the tube in the past, this is definitely easier! Snow can be a problem but generally only a couple of days a year on average.
Depending on what you're going for, £300k should get you something decent for the 3 of you.
Our DS went to local nursery and is now at local primary school. Only thing I would say is that if you finish work after 5pm, it can be a push to get back for 6pm to collect. A childminder may have better flexibility though.
I like New Mills as well and sometimes get the train from there although it is slower and more expensive. "No frills, handy for the hills, that's the way you spell New Mills" as they say.
Best of luck with your search. I moved back to Manchester after a stint in London and never regretted it. It's ace.