True staffordshire bull terriers used to be called the Nannie dog because of excellent temperament. But, they have been mixed with various bull breeds, many used as fighting or status dogs. I'd be very wary of adopting a staffie from a rescue centre because of that. One of my gentle dogs was attacked by a staffie who ran out of woodland, grabbed my dog and left 11 puncture wounds in his neck. They are strong jawed.
Lurchers are beautiful, usually gentle dogs. A friend rescued one from the sight hound charity. she's a gentle soul around the house, good with grandchildren but -she's killed two cats. She is now always walked on a long line, wearing a muzzle. My sister had a lurcher who never lost her high prey urge, so again, couldn't be walked off lead.
Its good that you are considering a rescue. Have you had dogs in the past? Do you have small children visiting ? Some breeds are easier to care for than others. You could use google to read up on breed characteristics but please, beware the myths about various poodle crosses. They can be fabulous pets but, the myths include, don't shed, easy to train, always good with children -none of this is always so, plus they're from breeds who love water, bred to retrieve from water so they love swimming and mud. their coats almost always need professional grooming every 6 - 8 weeks.. I've had two fabulous poodle crosses, one of them came to me as a pup, from a reputable breeder. He presented more of a challenge for training / temperament than any rescue dog I ever had.
My rescues have all been great dogs, all mongrel/x breeds but its harder to find them these days. the shelters are full of lurchers, staffs and old German shepherds. Very sad. You'll find though that after lockdown, there will be many young dogs/puppies needing adoption. So many people decided lockdown was the ideal time to get a puppy.
best of luck