You're asking one of those big questions that us old-timers call "$64,000 questions", actually, because there are dozens and dozens of different blogging platforms available nowadays and figuring out which is best for your needs is a non-trivial task.
First off, let's start by differentiating hosted weblog solutions from server-side solutions: a hosted solution is where you buy space on someone else's blogging platform and let them worry about running the servers, backing up the data, keeping it hacker-free, etc. A server-side solution is for when you already have a Web server and the administrative and IT know-how to install new software on your own system. The advantage of a server-side solution is that you have far more flexibility, but the cost of that flexibility is greater complexity. For most people, a hosted solution is a far smarter choice.
In terms of representative solutions, some of the most popular hosted solutions are Blogger, Typepad, and Yahoo 360. Server solutions are dominated by the Big Two: Movable Type (what I use), and WordPress, though there are many, many other software packages you could install on your system.
On the server side, the main difference between Movable Type and WordPress is the template language: because all blogging applications work off a small set of templates you develop or tweak to have the look and feel you seek, the ability to fiddle with the template is a critical differentiator between solutions. As far as I can tell, there are two main approaches to this template language: either a language that's emulating HTML/XML, or one that's built around the PHP scripting language.
Let me show you a snippet of each, so you can see the difference.
First off, Movable Type (and, by extension, Typepad, which is from the same company), looks like this:
<div class="posted"><a href="<$MTEntryPermalink$>">Posted by
<$MTEntryAuthor$> on <$MTEntryDate format="%x"$></a>
</div>
Not too dissimilar to HTML format, just add the "$" symbols.
By comparison, here's a typical snippet from a WordPress template:
<?php
if(isset($_GET['author_name'])) :
$curauth = get_userdatabylogin($author_name);
else :
$curauth = get_userdata(intval($author));
endif;
?>
Admittedly, they're not doing the same thing, but you can see that while WordPress is probably more powerful in as it offers you the full power of the PHP scripting language, it's also more confusing and much more geeky from a technological perspective. I like WordPress, however, because it's open source and there's something inherently cool about a commercial quality product you can download and run for free.
If you look at the hosted solutions, you'll find that they vary from being quite flexible but confusing (there's a hosted version of WordPress, for example, still in beta at Wordpress.com) to being simple but rigid, without any ability to do much more than change a few links and the name of your weblog.
Now, with all that said, on to your specific question. What you want to do is go into the templates and add your own code segments so you can include something like Google AdSense (not sure what that is? Check out my new article Getting started with Google AdSense) and similar.
My suggestion is for you to seriously consider using TypePad, to be quite honest. Even with their recent performance hiccups, they're still one of the best solutions available and they have the credibility as a commercial hosting platform to help you with your business goals for your weblog. Further, since they don't offer free accounts (like Blogger and WordPress.com) the overall quality of the weblogs on the Typepad site will inevitably be better, which can only reflect positively on your efforts.
Depending on how you want to integrate the content, you can also add material like an AdSense block by simply pasting it into the middle of your weblog entries. If you'd want to just add the code to the navigational sidebar of your Typepad design, you can do so by creatlng what TypePad calls a "Notes TypeList" (as documented here: Displaying custom HTML on your Weblog).
There are no solutions that make it as simple as clicking on a checkbox to include everything you'd like on your weblog in just the way you'd prefer, but with relatively little work I think that just about any of the paid services could work very well for you.
Long answer, but I hope that helps you out!
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Dave, I found your article realy interesting and I was wondering what you thought of http://www.terapad.com ?