My DD has been wearing glasses since she was 2, and I was also sad about it, but DD has never felt sad about wearing them. I am ok with it now, she looks quite cute with them on.
DD also has a lazy eye and is longsighted and we have hospital trips to see the optician, consultant and the orthoptist.
Depending on how severe her longsightedness is, she may well grow out of it. (My DS grew out of his longsightedness and didn't need to wear glasses after the age of 6.)
I found the first appointment at the hospital took the longest, as you'd probably expect. Once the initial appointment was over, we returned 6 weeks later, then another 6 weeks after that, then 3 months, then 3 months...then DD was given eye patches to treat the lazy eye, so we have to go back every 6 weeks at the moment to check the progress on the lazy eye.
The advice I was given to get DD to wear the glasses was to encourage her without making an issue of it. I was told most children realise that they can see better with the glasses so tend to wear them off their own back after a while IYSWIM. DD doesn't always put her glasses on first thing, but she will put them on before we go out and certainly wears them most of the day now. It does take time though, it isn't instant and the hospital wont expect her to wear them every hour of every day instantly. It does take a little time for them to get used to wearing glasses.
My DD is quite happy to wear her glasses now, doesn't fuss at all. (I have much more problems getting her clothes on to go out tbh.)
As for them breaking them, unfortunately they do get broken, although not as often as you'd think, and they can be repaired or replaced on the NHS.
It is nice to have a spare pair, but please be aware that if you ask for a spare pair, you wont get those on the NHS, and will have to pay full price for them.
OTOH, if your DD loses her glasses, she will get a replacement pair on the NHS. 