Rescuing a dog is a fine thing, but in my experience they all come with baggage. Many have been abused or neglected, and have behavioural issues that take a long time to work through (and may or may not be completely correctable). So there's that. If your friend wants a better chance of a non-naughty dog, a puppy is a safer choice.
Every dog breed has pluses and minuses. What kind of lifestyle does your friend have? Does she mind yapping? Shedding? Is size an issue?
I grew up with a beagle, and he was a sweet-tempered little thing, but mental when it came to food. Food ranked higher than anything else in his life, even people. My parents used to meet up with a "beagle walking group", and they'd share stories with other beagle owners about how naughty their dogs were when it came to food. Where the breed write-up says "hearty appetite", what it really means is, "will learn how to break into the fridge". And the shedding! And the absent-mindedly wandering off while following his nose! I'd never have another one, much as I adored him.
We had great success with our cocker spaniel/poodle cross. She was small, but not so small that you couldn't take her on a robust hike; she was loving and cuddly; she didn't drool; she was friendly with everybody (perhaps too friendly with strangers!); and she didn't shed. Downside? She had a piercing bark, and we were never able to train her out of barking like a maniac when someone came to the door.
If I had to recommend a purebred dog, I'd probably go with a poodle (standard or miniature, not toy). For a mixed breed, I'd go with some kind of poodle cross. There are lots these days!
ETA just read your last response, JAileen -- labradoodles don't have to be big. Mini labradoodles are really popular here. It's a small lab crossed with a miniature, not a standard, poodle. They are a little taller than a cockapoo, but usually not much.