To me, they're similar words, but "to choose" implies a larger selection of choices (if you'll pardon the pun) than "to select". If I was walking down the aisle in the supermarket, I would "choose" from 10 brands of fruit juice, but if there were two in front of me I would select one or the other.

They mean the same thing. "Pick" is also in this group. You can use any of them with the same meaning when it comes to a choice. However, normally when I use select implies time and effort in the decision. I looked at the alternatives and made the decision not to choose many of them. Instead, I selected the best one. I also do not normally select something which is known or personal to myself. This is because I already know them well. I don't need normally need to spend time and effort weighing the different alternatives. Pick is kind of the opposite of this. Normally there is no time and effort when you "pick" an alternative. Use this when you choose something which is the same as the other alternatives. "Choose" can be either. For example, if I offered you some candy you might choose or pick a flavor, but you probably would not select a flavor. You cannot really evaluate the alternatives without tasting each one, so you instead you would just choose or pick one. However you may have some knowledge of how the different colors normally taste, so its not totally random. If a magician asked you to choose a card, he would most likely use the word "pick". You can't see the value of the card, so any of them is just as good as any other. The choice is random, so the best word would be "pick". If I was taking a test with multiple choice answers, I would "select" one. I would evaluate A, B, C, and D, and decide which one correctly answers the question. I would probably not "pick" one. Choose also works fine here.