Lorna,
I moved to Chelt already with children (4 and 6 at the time) so can't help with the 'baby' stuff. However, notes on other stuff:
Leckhampton is mostly 'older' housing stock (Victorian terraces etc). Bishops' Cleeve has a lot of new estates. it probably isn't an issue now with you renting, but perhaps if your family grows and you want an affordable larger house, BC may serve you better.
Leckhampton 'village area' round the school has a couple of shops, access to Leckhampton hill allows loads of dog-walking space and there are good parks. A little bit closer in, but still not in the centre, is the Bath Road shopping area, almost like a mini town with shops and pubs and a thriving 'local' scene.
There is a choice of good primary schools in and around Leckhampton BUT they are very over-subscribed. Leckhampton has a small catchment area, Naunton Park was traditionally less popular but is so over-subscribed this year that they have added a 'bulge' reception class (making a year of 90) and there is STILL a waiting list.
As far as secondary schools go - beware! Leckhampton is mid-way between 2 excellent secondary schools BUT over the last few years has fallen outside the admissions area for both so children have been allocated less good schools way outside the area. From next year, the admissions arrangements have been tweaked to try to avoid this but unless the new Academy being built near Hester's Way becomes very popular and takes some pressure away from the exisitng schools, I would say that there is likely to be uncertainty about secondary schools for the Leckhampton area (particularly the 'village' area further out of town) into the future.
Pates' Grammar has no catchment area at all - children come in from a very wide radius, up to Worcester and down to Bristol. As a result, it is VASTLY over-subscribed and hyper-selective, I would certainly put no faith in a plan for your child's education that absolutely expected entry there. Children from the Leckhampton area also go to the single-sex Gloucester grammar schools. Children from Bishops' Cleeve would also be eligible for all these grammar schools IF they pass the grammar test.
Hope this helps a bit!