Does it matter what choices you make when training the artisan? Because I noticed that when I chose one option others disappear. Are they lost?
They aren't lost. The purpose of being able to select each item is so that you can open the "Details" panel for them. When you finally train, the artisan learns all of the recipes that were present in the list.
This is most clearly observed when training the jewel crafter. He'll show you the four jewel types that he's about to learn and you can browse the list looking at the details for each jewel type. When you finally train him, it's very easy to see (in the gem combining window) that he just learnt all of the recipes that were in the training window.