Unless you are particularly short or have short arms, you might not need a "ladies" rifle.
My wife is about 165-170cm tall and she can shoot my rifles just fine.
If budget constrained Howa is a good option, lots of used ones on TradeMe for cheap and there is a youth stock available if the LOP (length of pull) is too long.
I'd spend less money on the rifle and more money on the scope, and I'd be looking to by used.
As for cartridge, 243 or 6mm Creedmoor is a good option, or even 6 ARC if you get a Howa Mini.
With good shot placement a 6mm bullet is more than enough, and a big cartridge in a lightweight rifle will be more likely to give you a flinch which will not be good for shot placement.
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