Whether you have an emergency stash is completely up to you.
If you do choose to pump, I'd suggest first thing in the morning - women tend to have the most milk then so there's some to "spare". (I can pump and feed my babe right afterwards in the morning and she still gets plenty.) I know a lot of women feed on one side and pump the other, but I'm not coordinated enough for this trick.
If you pump regularly, then your body will produce more. If you pump a few times just to have an emergency stash, and spread out those pumping sessions with days in between without pumping, it should not really have any noticeable impact on your supply. It's not any different than if your baby was just a bit hungrier that day.
Milk lasts 3 months in a conventional freezer or 12 months in a deep freezer. If you're just pumping a small amount, you don't need to bother with storage bags - just freeze directly in the bottles. Usually pumps come with a few bottles, so if you buy a pump, you'll have everything you need. I agree with the pp that a manual pump is best for such little use.