Mrs F is the most reluctant cyclist in the world and doesn't have a bike - however is willing to get a bike and try it again for the kids sake

We're looking to buy a bike (most likely second hand) but not spend a lot in case she doesn't use it that much, hoping for £100-£150 or so (budget can be increased if unrealistic). Main requirement is for it to be as light as possible I think but seeking guidance?
Usage is likely to be paths and trails mostly. She has visited a shop to get sized and will apparently fit a 16" frame.
Any advice on manufacturer or style and places to try much appreciated. Have tried gumtree but there's not much info on the bikes spec/weight etc.
Ta in advance
Alistair