Renstar, firstly, you should always rinse your bottles, pump etc in cold water first, and then warm water. The cold water rinses most of the milk away so that the temp of the warm water won't multiply the bacteria.

Also, I agree with Sushee. Bfing can be difficult in the first weeks/months. Trying to learn how to express, and fit expressing into the feeding schedule you are developing can be really tricky. I'd master the bfing first and then you can think about expressing down the track. When you do express, you usually store it in breast milk storage bags or breast milk storage cups, and baby will drink from the bottle (or a cup). Some people store it in bottles but they take up more room.

You will learn this at the bfing class too.