My friend has
this guitar it is a full size and he has the steel strung version. Tone is lovely, built in tuner and a good all-round guitar. Granted I know he can play so, to learn on maybe different.
I had my first acoustic as a cheap fender and still use it 15 years later!
My Electro-acoustic is
A Lag not the most common make and not the best guitar but actually has a lovely tone and you can hear it
here (click listen now and its the track ordinary song)
It depends on what you daughter is learning, if she is going for rock guitar then these two are not right for you at all, you can pick up some yamaha starter packs for a reasonable price and they are good(ish) guitars.
If you are looking for a guitar alone then
Gibson |Gibson Ibanez
You do get what you pay for and a guitar is a personal thing.
She has to like looking at it as well as playing it.
I suggest that you take her to a shop to get a feel for what she likes.
The trouble is you have guitars like Daisy Rock that are not great guitars but are a cool shape (pink flower, hello kitty)
It is an investment so if she is serious about playing spend as close to that £300 budget that you can and you (she) would not be disappointed.
Remember that if you do the electric route she will need a practice amp to hear what she is playing.
Ebay might be your best bet as you can get mini amps very cheap and just let her build from there.
(If she wants to be in a band?? Then the amp needs to be much more powerful but we can cross that bridge later

)