I think the 12yr old bit is irrelevant – what bike for a 5ft girl.
Something light and not expensive is moon on a stick as money mainly buys you lighter components.
I’m about to have the same issue with my daughter and am probably going to wait until she can ride a small framed bike – whether it be women specific or not.
Then it’s going to be a matter of how much we decide to spend. I’m tempted to buy something second hand so it not a big deal if it gets dropped, you get more for your money etc.
So I’d get her leg/torso measurements and/or visit a bike shop so she can sit on a few, Then look at ebay etc.
I’m going to struggle to buy something cheap as kids tend to respect decent equipment and I’ll make her look after it and lumber her with the problem of never being able to ride a cheap bike again.
Let us know what you end up doing.