Let me answer your questions, not necessarily in the order you asked them.
"2) Should I stay in London and take several different guided day trips to fully embrace the area?"
Check out www.walks.com. The London Walks company has a day-long trip to the Cotswolds, and they are one of the best, small group; you meet at Paddington Station with the leader and take the train. The group leader takes you to several villages. Directly to their Cotswolds page: http://www.walks.com/Standalone/The_Cotswolds_%E2%80%93_Sightseeing_Tour_%E2%80%93_Guided_Walking_Tour/default.aspx
"1) Should I stay in Cotswold - rent a car in west London on Sunday to avoid congestion fee or take the train to Oxford to rent a car in Oxford on Monday?"
"3) Should I take a train to Oxford, get a B&B and use a local based guide service? "
If you want to stay in the Cotswolds, skip down to the paragraph near the bottom of my post. If you are wanting specifically to pick up a car OUTSIDE the Cotswolds, or looking for a base to stay OUTSIDE the Cotswolds, keep reading this paragraph. I had personally rather take the train to Bath, rent a car there, and drive to the Cotswolds. (not far) Renting a car in West London or Oxford is too much traffic for me. Maybe not for some other people, but for me, I want to get out far from London before renting my car. Bath is easy to reach, just 90 minutes from London Paddington station by train. Bath train station is located in the city centre, just a short walk from the shops and attractions and car rentals. There are B&B's and plenty to do in Bath, also.
"3) Should I take a train to Oxford, get a B&B and use a local based guide service? "
"I prefer not taking a large guided tour bus, so if anyone knows a small, local reasonable guide service - that would be a bonus."
If you just want to do day trips to the Cotswolds, and want to stay somewhere besides the Cotswolds, I would prefer Bath. Out of Bath the tour company:www.madmaxtours.co.uk runs trips on a small comfortable mini-bus to the Cotswold villages. They also have a Stonehenge day trip out of Bath, in case you get interested in that.
You originally spoke of wanting to spend all 3 days in the Cotswolds. If so, take a train from London Paddington to the Cotswolds (Moreton-In-Marsh, trains take about 1hr 30mins and go roughly every hour), check into a B&B somewhere like Moreton-In-Marsh, and there are small private car/van services there that will take you around to the other villages. Or you can rent a car there; Moreton-In-Marsh used to have a car rental place. Let me check if they still do. Will come back here with correct location.
You could also take a taxi (or drive your rental car) from Moreton-In-Marsh to Chipping Campden (not very far) and stay there. It is a pretty village. Here is their website: http://www.chippingcampden.co.uk/contentok.php?id=193
You can't go wrong staying at The Eight Bells Inn. http://www.eightbellsinn.co.uk/stay.html
Broadway is another beautiful village nearby, good location for side trips.
Hope this helps.
