When it comes to JPEG compression, there's really only one thing to know:
Compression = BAD. Avoid it at all costs.
Now, there are those who will disagree with this statement: web designer geeks out there trying to make things load super fast for people with slow dial-up connections and they don't much care what the pictures look like.
But that's not you. You are a regular Joe/Jane who is going to make a photo book from your vacation pics or put a few scans in your personal history. So for your purposes, I'm going to show you how to NOT ruin your photos.