If you have noticed; pick, choose, and select are all synonymous. They have similar meaning. They can be used interchangeably, but I have noticed that pick is more often an informal way of saying choose. And choose a more informal way of saying select. In everyday English, you will hear choose more often than select. And pick more often than choose. Pick can be a tool or a verb. Like ‘pick where you want to eat.’ Pick up is the actual action of grabbing something, ‘pick up that toy.’ Pick out would be most similar to choose, ‘I need to pick out an outfit.’ Though, pick out is sort of a more formal way of saying pick. I hope this may help.

'Pick up' can mean a few things. It usually means to take something from somewhere low, or to collect something from somewhere: Pick up those clothes from the floor! Can you pick up a bottle of milk from the supermarket on your way home? 'Pick up' can also mean to receive, in the context of radio signals, or other communications: I can only just pick up that new radio station in town. 'Pick up' cannot be generally interchanged with either of your other examples. There is not much difference between 'pick' and 'pick out'. 'out' in phrasal verbs generally gives an idea of 'thoroughly'. If you pick something out, it means you deliberate more about your selection. So, they are interchangeable, but 'pick out' has an extra implied meaning of 'more consideration and thought'. You can pick one flavour of icecream. / I'll have the Apricot Ripple. I need to pick out a new dress. I like the white one, but it will be hard to keep clean. The green one is nice, but I don't think the colour goes with my skin. The short one is a bit too revealing. 'Pick out' can also mean to distinguish. We are so high up, that I can't even pick out my house from here.