Beginning Sept 2014 I hope! I don't know Oxford Ramblers, but each area has a Ramblers group and they are usually good.
http://www.ramblers.org.uk/
The long distance national trail
The Thames Path passes through Oxford, so you will be able to do some nice walks on that heading out of the city in each direction.
Oxford sits between the Cotswolds and the Chilterns, both fabulous walking areas. I don't know the Chilterns but I do know the Cotswolds. You can take a train from Oxford to Kingham and Moreton on Marsh. Both will have good walking paths. I am sure there are buses into the Cotswolds, just make sure you have their timetables as sometimes they do not run often. You could take a bus to Burford, the eastern gateway to the Cotswolds, and walk from there. I think you are going to be spoiled for choice.
For transportation options use
TravelineSW - you can get bus schedules from that site. For trains use
TheTrainline.com. If you do a long walk out of Oxford, you could call a taxi to get back to town if bus or train doesn't work.
Get an Ordnance Survey map for your area and nearby areas. And some walking guidebooks. I have some
information about walking on Cotswolder. For the Cotswolds I like the Goldeneye Cotswold Classic Walks, but you may want the more detailed Pathfinder Guides. There will be one for Oxfordshire. You can get all these things once you are in Oxford.
Oxford is a very nice town and has good train connections. Trains run every 15 minutes to London and are not expensive (trains to London can be shockingly expensive - as they are from where we live). You can probably figure out some good day trips to other areas for walking.
You will get rain, but there will be many fine days and breaks in the weather. Make sure you have good walking gear.