You could modify index.php for starters, and then go from there.
Take out the RSS feeds, although I personally like them since it's one way to make sure users get information from your site that they may need to know, then pretty much just reformatting the content of the dashboard to make it more like what you would like.
From the "end user" standpoint, a lot of them like being able to see people who have recently linked to them, as well as a recent list of comments. Recent posts are helpful on a multi-author blog, too.
Have you considered perhaps a set of assistance pages, which explain different areas available and what they do? Thus instead of "taking away" information for everyone, it empowers less knowledgeable users with information about what their site can do.
My "fix" in regards to the admin area between using TA and what I've done now was simple, but it worked well. I reformatted a little of the admin css file, and added 2 new classes.
In a nutshell, I moved the sub-menu items over to a list down the left side. Mainly because if you have a few plugins activated, it can get pretty cluttered up top. The sub menu is generated in an "if" statement, so I set a variable prior to that, that had the original class name for the main admin div that holds all the content (wrap). Then in the if statement I overwrote that var with a new value (wrapsub).
Then, I went through all the admin files and found where the class was set to "wrap", and had it echo the value of the variable I set.
This effectively narrowed the "wrap" div, so that if there was a sub-menu present it had room on the left.
It worked, and made an easier presentation for less savvy folks, yet all it did was move a few links for those knowing what they were looking for.
The reason I moved away from that was I got tired up updating and merging all the files when upgrading. Granted I still have to do so for some stuff, but it's a whole lot less than it was.
I'd like to see a theme system just for the admin area, but it's been something discussed over and over since "back in the day". The priority seems to be front-end first, which is understandable. That's where 90% or more of the "action" is.
The backend has come a long way though, although "less savvy" folks still have some adjusting to do with it. But then again, that's the case with anything, is it not?