Reading about 10.1 is kinda pointless, as OS X has changed a _lot_ since then. You'll really never need to worry about Classic, as it was designed for people coming from Mac OS 9 and earlier that needed to still run their applications. OS X was a total re-write, so they added "Classic" as a way for people to still run their OS 9 applications through OS X. Pretty much no one uses this anymore, as all of those applications are native on OS X these days. You won't need this
You are right in that OS X does not run .exe applications, as those are Windows applications. I definitely want to make sure that you know OS X does not natively run Windows applications, and not every Windows application has a Mac version. For example, Winamp doesn't have a Mac version, so you wouldn't be able to use that on OS X, unless you use Virtual PC, which runs Windows on top of OS X. However, while there is no Winamp, there is iTunes. Fortunately, iTunes is really awesome
With that said, there are Mac versions of many applications, such as Photoshop, Firefox/Mozilla, Dreamworks, Acrobat, etc etc.
Let me be more specific about the applications you'll probably want to look into, based upon what you said you used your computer:
For media players, iTunes is ideal for MP3s/AACs, VLC is a great all-in-one movie player (supports DivX, etc), Quicktime allows you to change media formats (i.e. turn a movie into an MP3), and Apple's built-in DVD player is perfect.
For instant messaging, Apple's built-in iChat is the best AIM client you'll find (far better than AOL's AIM client), there are versions of MSN/ICQ/Jabber/Yahoo IM from their makers natively available on OS X, and there are also a bunch of third-party IM clients that support multiple messaging services at the same time. One example of a third-party IM client is Adium, which is is _very_ customizable (see
http://adiumx.com/images/actionshots/adium-3.jpg and
http://adiumx.com/images/adium/overview.jpg and
http://adiumx.com/images/actionshots/1081482691.jpg for examples), has tabbed IMs (i.e. multiple IMs in one window), supports AIM/ICQ/MSN/Yahoo/Jabber, and has very nice log management. Totally free, of course. Although, I tend to use only AIM, so I prefer iChat, as it's really the best AIM client there is.
For image editing, you have a number of options. If you're looking for an awesome photo manager that synchs with your digital camera and has basic editing abilities, iPhoto is perfect. However, if you use something more powerful like Photoshop, you'll be happy to know that that's natively available on OS X. iPhoto can use Photoshop as its photo editor too, so that's sort of the best of both worlds. There are a number of different applications in the middle though, but those are the two most popular.
Finally, for web browsing, there are also a million options. Apple's browser, Safari, is my personal favorite. It's very fast, renders pages perfectly, supports pretty much every web standard, has tab support, popup blocking, built-in Google searching, a fantastic bookmark system, and so forth. Then there's OmniWeb, which uses Safari's engine, but adds a bunch of features like visual tabs, RSS viewer (Safari 2.0 will have this), and some other things. If you're using Mozilla or Firefox at the moment, you'll be happy to know that both are fully available on OS X and look and work perfectly. While Microsoft's Internet Explorer is available on OS X, that's really something you should stay away from -- on any platform. IE is really the most outdated browser, even on Windows. Safari is definitely my favorite.
You hadn't mentioned an e-mail client, but let me just quickly say that while Outlook (called Entourage on OS X), Eudora, and Thunderbird are all available on OS X, Apple's on Mail is really the best e-mail client. It has awesome spam filtering, great e-mail organization abilities, and uses Safari's engine to render HTML e-mail.
By the way,
http://www.macupdate.com is the best Mac software download site.
Finally, let me answer your task manager question. OS X has the Dock, which is a very innovative (and cool looking!) approach at replacing the task manager, and it does an awesome job at it. It's an all-in-one bar that allows you to launch applications, see the ones running, see minimized applications, quit any of them, force quit if needed, and so forth. You can also do stuff like dragging a folder to the Dock, right clicking on it, and basically using it as a quick-launch for the contents of that folder. When right-clicking on an application in the Dock, you can quickly access important functions of it. For instance, if you right click on the iTunes icon on the Dock, you can play/pause/rewind/fastforward. Other neat features include the ability for applications to dynamically display information in the Dock (for example, the Mail icon has a badge on it that shows you the number of unread messages), and if you minimize a movie to the Dock, you can actually have it continue playing down there. The Dock takes a few minutes to get used to, but once you do, you'll see just how powerful of a setup it is.
I'd love to show you a few screenshots of things I've talked about so that you can get a visual example of them. If you want to, feel free to message me on AIM (screen name is g0rman -- ignore the away message), and I'll show you whatever parts of the OS or applications you want to see.
You're my hero 
