Customer:a person who purchases goods or services from another. is also called a buyer.
Client is also a customer. But the term "client" is mostly used for a person or group that uses the professional advice or services of a lawyer, accountant, advertising agency etc.
Choose : To pick from a number of options.
Select would be to pick in preference to others.
Let me give you some examples:
1. She chose Monday to travel.
2. She selected the brown dress instead of the blue.
3. This CD contains selected features of the tour.
Hope this clarifies.