Congrats on your new little fur ball.
55- 72 is the best temps, and as long as it's dry the basement is fine.
So as not to stress her let her come to you. Open the cage door and see what she does.
Offer her a treat and a dust bath, but don't force anything onto her just yet.
I like to give my customers something from their cage like a house,tube or piece of fleece that they are used to.
Give her time to get use to the new smell, sounds, and surroundings.
Don't change anything with her feed until she is settled.
Don't give her too many treats.
They have their own little ways of telling you what they want and don't want.
For the first couple of weeks pay close attention to her behavior, eating habits, and her out put.
This way you'll know if a problem should arise.
If she's pretty tame she may not mind the move and be very happy with all the attention.