My son was almost 3, as well, when we moved him from a crib to a big boy bed. We were lucky, too, in that he had never tried to climb out, and was a pretty good sleeper. But, we needed the crib for a new baby girl that would be coming soon.
As for how long it will take for them to adjust... it's probably a little different for every child. For Joshua, he was nervous about sleeping in it for the first couple of nights because he was used to the confined security of the crib. But, after a few nights, he realized that he could get out of bed and start playing with his toys! At that point, he stopped being nervous about sleeping in it. However, we did have to start dealing with the issue of him getting out of bed when he wasn't supposed to. And we still do deal with that some, but I think that's just part of parenting! We just do the best we can!
With the potty training, it would probably be a good idea for her to be in a bed that she can get in/out of anyway. That way, if she happens to feel so inclined to start using the potty more, she can get out of bed if need be to do so, instead of the only option to be her diaper or pull up until someone comes to get her.