I'm an empty nester in Doubleview. My own long term pets have passed on so I have lots of spare love and care available for your pet. I have been house and pet sitting since 2011 and I have looked after all sorts of animals including many different dogs from cheeky chihuahuas to independent Maremma Sheepdogs. With dogs, I have found that with a quiet introduction, a gentle pat/scratch and maybe a little treat, dogs respond well to their new carer. After that, we are pals and it's off for walkies, a play, and a companionable sit/curl up.
For cats, I would start with putting your cat, its bed and litter tray in the laundry. The laundry opens onto an open plan lounge/dining/kitchen area where your cat can explore and settle in. The laundry also opens onto an outside area which is enclosed by a cat net with plenty of room for puss to wander and find a sunny spot. I will keep puss company and we should be friends in no time and ready for head scratching and tummy tickles. :-)