I live in woodley, which is a fairly mixed area, it has good links to the train station and the m4 to be easily commutable to London (you can catch a direct train to Waterloo from Winnersh or Early both less than 5 minutes away, or catch train to Reading for fast train to Paddington, or drive to twyford less than ten minutes away and catch the slightly slower train to Paddington)
You would be able to buy a 3 bed house for £250k, there is a lack of older houses in woodley so would be mainly new builds or 70'/80's. We have a large shopping precinct with Waitrose, Iceland and Lidl in, as well as newsagents, fabric shop, book shop, card shop, robert dyas, clarks and cargo.
Woodley comes under Wokingham Borough and has some fab schools. The girls grammar school is Kendrick and that covers a huge area and so is very competitive to get into, so you'd have to do a lot more research to see if your dd was likely to get a place or not.
To the other side of woodley you have Winnersh and Wokingham, again some very good schools, but some dodogy areas and £250k in those areas is likely to put you in the less desirable parts (a quick look on rightmove confirmed this). Wokingham has a town centre with supermarkets, clothing shops etc in but is bit run down at the moment, which is very surprising when you look at the housing. Again good links for London.
The other side of Woodley is Earley, Earley is a nice area, a few parks and again good schools as comes under Wokingham council. Some shopping, a large asda and a small precinct with pet shop newsagent, post office and take away. My parents are in Earley and I was born and raised there, its a bit more expensive than Woodley though hence us moving to Woodley for a larger house. Lower Earley is all newly built (well since 1980's and they keep adding) so you'd still get the school catchment areas but its a much more densley populated area than Earley, Woodley and Winnersh.
When i first moved back to Reading we lived in Whitley for a while, never again. We were broken into three times nd car stolen/broken into. the schools werent great, but it may have changed in the last 13 years.
Tbh i don't think Caversham is all is made out to be, the schools arent very good and the housing expensive. They also have a large less desirbale areas, but for me it was the lack of good schools that put us off moving that way.