I ride ss (well i did until I got pregnant) and I love it! That being said I had well and truely got the riding bug already. But I did enjoy it more than riding a geared bike for a good few months (although being fit and light helped!)
Main pros for ss I reckon would be:
Its cheaper so you should be able to buy her a cheaper and lighter bike for the same cost.
Its simple, so less faff and fewer things to break or get annoyed with!
Less likely to get in a muddle with gears and stuff if its all a bit new.
Attacking techy bits might really boost her confidence and improve her riding
Main cons:
Could get frustrated with not getting up hills...
Rather than attacking things in the ss gear (where you could perhaps spin over it in a lighter gear) she might chicken out more
Not sure if that helps, but those are things that spring to mind. I found riding ss massively improved my riding, teaching me to attack stuff and generally be a bit more aggressive. Also taught me to maintain more of a flow and stay off the brakes a bit more. But it is a bit of risk if she isn't into riding already... perhaps a 1x9 set up might be a good compromise?
Whatever you do though, I'd definitely get the bike as light as possible. For us 'weaker' riders, weight can make a massive difference. If at all possible get a nice light wheelset (shouldn't need to be that strong) and a light fork too (again, doesn't have to be the best - just light enough that she can loft it over roots and rocks). These make the biggest difference imo.
I definitely think its worth spending a bit of money on making the bike as good and light as possible within budget, as sometimes the effort of dragging a heavy bike up a hill is all that stands between someone loving and hating riding! (I speak from experience!)
Plus, if you get it all secondhand you'll probably be able to get your moneyback in a few months time if it doesn't work out. Well worth trying im my opinion.
(I feel so strongly about giving her a chance in fact, I'm tempted to lend you a decent pair of forks for a few months!)
Anyway, I hope that helps!