Sounds like you've already spent some time with Page Builders --> Menu Builder. That's the menu layout. There is only one, you edited by dragging those boxes around. Why it looks hairy after logging in is the buttons you've lost to "shows for guests only".
For Example, The first 5 things in the menu are Home, Join (says Account), Dashboard, MyProfile and Mail.
The display state is what makes the layout LOOK different depending on if you're logged in or not. The UnSeen ones are crossed out here.
If Logged in you'll see : Home | Join | Dashboard | MyProfile | Mail | People | For..
Not logged in will see : Home | Join | Dashboard | MyProfile | Mail | People | Forum..
It looks now that your guests menu is [Home Join People Forum] etc. But it's the exact same menu as your members with visibility toggled to suit.
Once you've dragged things around to the right order, then you "enhance" your display for members or non-members by turning visibility on or off. Then if you're like a lot of us me, you'll spend untold hours effing it up, then come back and look for the automatic reset to defaults. Cuz it's seriously a pain to fix if you stir it up too much, and the defaults start looking pretty good!
Now, the other builder, the "Member Menu builder" is for that bar that is normally on the bottom of the browser frame. Whole nuther ball of wax. "Top" is the two buttons on the left, usually username profile link, and status button. "Top Extra" is the links on the far right end of the bar.
As for your Q about changing the dashboard, the actual "dashboard" page is called "My Account" and can be edited for layout in page builder, select "Account" from the dropdown menu. Only shows the boxes that display though. I'm not at all sure on the order of the menu that displays on that page though. (home avatar, activity, my membership, privacy, subscriptions, etc) might be a default thing with order controlled in the DB or the html for that page. Someone will know.
Edit: Dayum, I went thru all that to find already answered. I'm going for a beer. back later. lol.