Facebook now doesn't show me all my friends' updates, just what "it thinks" is my friend. I don't see posts on my timeline from people that I care about. I understand I need to change what appears on "edit options", but all I see is just "hide posts from" not "show posts from everyone". How do I do this?
There are a couple of settings you can adjust to change what and the order in which you see content in your news feed. In Facebook's Controlling What You See in News Feed the first method suggested is changing how you sort stories in your news feed (in your case you would probably want "Most Recent" to see stories from all of your friends in order of recency):
You can also Filter by friends list (which it sounds like you do not want to do, so make sure this isn't selected) Filter by friend lists
As you mentioned you can also hide or unhide stories.
You may want to check to make sure your settings include all stories since some users seem to have only close friends selected by default (see Facebook Changes News Feed Settings, Some Users Only Shown Close Friends by Default) I should note, however, that I wasn't able to find the interface shown below, so these adjustments likely are made in the previously mentioned sidebar where you can select sub-lists of friends
For the new news feed layout (circa April 2013 according to Mashable's How to See EVERYTHING in Your Facebook News Feed) the interface looks like this: