My wife and I walked the Warden's Way (Lower Slaughter to Winchcombe), and then the northern part of the Cotswold Way (Winchcombe to Chipping Campden) at the end of May this year. The weather was amazing--only one 30 minute shower the whole trip, with weather in the 15-22 celsius range (60s to low 70s?). But I think we were blessed with such an unusual stretch of sunny weather. I'd be prepared for weather from the upper 50s to low 70s. We dressed in layers to adjust to different temps and rainfall. I usually had shorts, a thin non-cotton undershirt, and a long-sleeve non-cotten outer shirt (I also had a fleece for colder weather, though I didn't need it as much), and we used ultralight raincoats (from REI) as either windbreakers or for rain (they did come in handy for the one shower we had, a pretty strong one). We packed light enough so we didn't have to use baggage service, but we had to sacrifice variety and handwash every couple of nights, so it's really up to what you want out of it. Many people use the baggage services (especially on the C2C route), and I'm sure that would be nice, to be relatively unencumbered.
On the part of the Cotswold Way we walked, there were some rather steep hills, but it was never a case of having to "climb" and I never felt the "scared of heights" feeling I sometimes got in the Lake District when descending the fells.
I'd have to leave to others (try a google search, there are a few websites out there with peoples' diaries of their walks) their opinions on which direction to go, since we only walked a rather short section. (By the way, I'd heartily endorse "North Farmcote B&B" as a nice place to stay; although it is 3 miles outside of Winchcombe. "The Mount Inn" in Stanton was a great place to take a lunch break, and the breakfast at "Learmonth House" in Broadway was the best of our entire England trip.
I hear that the southern part of the Cotswold Way has fewer B&Bs, necessitating longer walks, but for the Winchcombe to Chipping Campden section it was 2 easy day walks. You might want to slightly increase your "training walks"--especially if they don't involve hills.
Best wishes & happy planning!