I am no expert by all means in this area (I know I have owned cats but never a rescued nervy one) but I'll try and advise you,others on here will definately have a better idea of how to help than me.
For starters THANK YOU for taking this cat on.
Firstly we have to remember shes just lost her owner whos shes been used to for the last year and shes been with a family who eventually have decided they didn't want her,the poor cat doesn't know where she is so obviously shes going to think that your not to be "trusted" yet so she will be weary about giving you any kind of affection.
I have always been told never to look a cat directly in the eye as they will then see you as a threat,leave her come to you (this may take weeks but eventually it will be rewarding) and when she comes near you talk to her but don't go and pick her up,take things slowly by stroking etc but if shes walking around the room don't have direct eye contact with her only if your talking to her have eye contact. You could try having her come to you for food that I would of thaught would be a good place to get her to trust you (but others will have more experience here than me).
I don't know if anybody would recomend keeping her confined in one room for the time being while she gets used to you,one big house seems a big challenge for her and maybe she needs to be confined to once place first? This is just an idea,don't try it without somebody else giving you the go ahead.
As for the grooming,I wouldn't worry too much about that yet,you need to get her to trust you first before you do anything like that and tghat could take weeks but please be patient,the poor little thing must be so confused at the moment and needs somebody who is patient and will give her the love and care she deserves
Like I said I am no expert and others will be able to help more I am sure.
All the best and we need pics of her as soon as you can please,we are suckers for pics in this forum