An adult Standard Poodle from a shelter is usually friendly, family-friendly and good with other dogs. Because it's very sensitive and people-oriented, it often suffers in the shelter from the loss of its people. Give it time to build trust – thanks to its extremely high trainability, it learns new rules in no time once it feels safe.
Health is worth a close look, too. Standard Poodles are considered robust but have a clear pattern: the joints, the eyes and the risk of gastric torsion (bloat) often remain issues for life. Breed-typical issues include hip dysplasia, elbow dysplasia and patellar luxation, as well as eye diseases such as cataracts, ectropion / entropion and progressive retinal atrophy (including the PRCD-associated form). Neurological diseases such as degenerative myelopathy or neonatal encephalopathy with seizures, and the skin disease sebaceous adenitis, also occur in the breed.
A health-focused breeder (for example in the Deutscher Pudel-Klub e.V., Germany's Poodle club) has the parent dogs checked for joint and eye problems by X-ray and clinical exams to lower the risk for the puppies. For hereditary defects such as prcd-PRA, degenerative myelopathy and neonatal encephalopathy, they use established DNA tests: these show whether a dog is clear, a carrier or affected, so carriers are deliberately only paired with clear partners. But if the shelter dog is of unknown origin or comes from a puppy mill, these screenings are missing. So make regular vet checkups and joint-friendly exercise a fixed part of your plans.