My Mum lives with us, we did what you are thinking of so she has her own living room, bedroom and bathroom all downstairs and we have our bedrooms, bathrooms upstairs then our living room downstairs and share the kitchen/dining/conservatory which is one long room.
It works well for 90% of the time, we agreed before we did it that we would live separately but under the same roof so we do our own thing, she cooks her own meals for herself the majority of the time but sometimes we'll cook and eat together.
We have divided the cupboards and drawers in the kitchen and the shelves in the fridge between us so we have our own things.
With the bills she contributes 1/3 and the house is in mine and dh's name.
Regarding care so far she doesn't need any, she's early 80's and so it might be something she needs in the future but she's always said it's not something she'd want me to do, she's a private person and would prefer to pay someone.
Of course I'd do things like her cleaning and errands but I'd do those anyway if we didn't live together.
It's been lovely for dd's to be bought up with their Nan in the same house, it's meant they are incredibly close and it's been very handy for me to be able to pop out and leave the kids at home instead of having to take them with me.
The downside is that she's tidier than us so there have been a few rows over that which remind me that I live with my Mum and in turn I don't feel like an adult at times, it hasn't happened that often over the 11 years we've been together but I do sometimes wonder if my life would be different if my Mum didn't know where I was 24/7.
On the whole though the good definitely outweighs the bad.
You say that you would have a communal living room but I'd advise against that, you need space during the day for yourself and so does she, you need to be able to put your feet up, watch what you want on TV and talk to your dh without your Mum listening.
You could maybe look at somewhere that has a large living room you could divide in half or a garage that could be converted into a room or a bungalow where you could add bedrooms upstairs then use the dining room downstairs as your living room.