The new search dropdown is what I am excited about. I know that the operators were always there and advanced search was a click away, but what can I say, I am lazy.
I'm lazy too, and that's why I prefer to type in keywords rather than having to tab-tab-tab-tab-tab until I get to the relevant field or worse, having to grab my mouse to select the kind of search I want to do. It seems it will still be possible to type directly keywords in the field so it's okay. I hope they also let all the key-binding (for instance, '/' to focus the searchbox).
Now, let's hope that the next step is not to make Gmail just a Google+ app, like they did with Google Reader.
Hopefully they'll leave in the ability to just type in your boolean search. I prefer that method as well and send myself a lot of email so I'm often searching for stuff like [from:me has:attachment]
Which is the best way to learn those operators. The shortcut "/" to get to the search box is probably what I use the most, and writing "from:john to:mailing-list" is such a great time saver, if you compare to other mail clients.
What I use the most is [j]/[k] to move between email from the inbox while using [x] to select some messages which i [shift]+[i] to mark them as read and the [e] to archive. I think I easily do that with half of my emails for which reading the subject (and sometimes also the little preview) is enough to know that I don't have to read them.
I totally agree, except that I tend to use [y] to archive, since it also does the "right thing" from views other than the Inbox (e.g. removing label "Todo" from selected emails when viewing all emails with label "Todo").
I also use [ and ] a lot. From message view, they archive the current message and immediately move to the previous/next message in the current list.
I use J/K to browse so much that I sometimes forget it's not built into all websites. "What do you mean I can't hit the letter "O" to open that link??"
Now, let's hope that the next step is not to make Gmail just a Google+ app, like they did with Google Reader.