We've started combination feeding with expressed milk, so I express around the time that my partner gives her bottle so that my boobs don't become too full by "skipping" a feed. That then produces milk for the next few days/adds to freezer stash. It's a good idea to gradually get baby used to bottles and switching between breast/bottle so if I had to leave her for a longer period I know she'd be fine taking bottles.
My health visitor said to try first thing in the morning and that worked for me. It won’t affect your supply if anything you’ll be producing more x
Depending on why you're expressing, I express once in the morning a few times a week after babies first morning free as the morning is when your supply should be highest but I am expressing just to have a bit of a supply for when someone else needs to look after him.