Great question and will get many different opinions. Both my boys used a "binkie", yes, mean ole' Mr Moon took them away. I had worked for a pediatrician in the past and he had a logical analogy ... when babies come into the world, its a very over whelming world and if their waking hours are with consistant nurturing, showing them off, having them sit up on your lap and letting them look around (just a few examples) they become overloaded on what they have focus on trying to take it all in and they are searching for a way to settle themselves down. Binkies are a good thing, rocking is a good, patting them on the back (just a few examples). Yep mine loved to suck its soothing for them, mommy had only so much milk to give than I had to go to the cereal spiked formula ..
.. There is not a thing wrong with a binky and before you know it they will either love it more or give it up.
As for the thumb and or finger, they never go away, they are part of the package and so much harder to divert a child when the thumb or finger is at arms reach, no punn intended. It's very settling and soothing for a child as long as it is not used for a substitute.