Goose I have had Rescue and pedigree dogs. My first dog that I could truly call my own was from the Dog's Home, when I was 14. A scrawny puppy who was quite sickly, got distemper (twice) which I nursed him through, against the vet's advice. He was the most amazing dog, very bright, had some collie in his 57 varieties. As he got older, he developed epilepsy because of his illnesses as a pup, and had to stay on medication. Dogs' Homes are more particular about healthcare now, so the pups get immunized. A Rescue puppy would be a good bet.
I would hesitate and find out as much as possible about a Rescue adult dog, whether from a Dogs' Home or breeder, as some dogs have behavioural problems that might not be acceptable to you. It all depends on why they have been sent to be re-homed.
We had a Rescue clumber spaniel who had been show-bred, then left neglected in the breeder's kennels when a better litter came along. She was aggressive with chidren when they had food, and we reluctantly returned her to the Rescue breeder, after falling in love with her. We coudn't trust her after she leapt at a child's face for the crisps he was eating. She was re-homed away from chidren. We then bought a clumber puppy from a breeder with integrity, and she was a delight.
Special Rescue organisations like Greyhound Rescue seem to do a great job, with dogs that are perfect for older owners. Depends what sort of a dog you're looking for.
We've had spaniels, collies and German shepherds over the years, and when I retired I wanted a dog who would be great with my grandchildren. She is a basset hound, patient and loving, perfect with chidren, stubborn as anything, and likes things how she likes them - if I move her manky chewy bone, she retrieves it and puts it back where she left it! 
If you get a puppy or older dog now, you will still grieve for Mystery - why wouldn't you after all she meant to you? But a dog is a great comfort and companion, and there are so many dogs in need of a loving home. I hope you enjoy finding one when the time is right for you, whether that's now or later. 