Lots of questions, but I'll do my best. Look in the sources section for links to everything I will mention. Unfortunately, there was no new Mac Mini announced at Macworld, but it's still a nice machine.
You'll want to get Boxee, which is a full screen media center application that let's you stream from sites like Hulu, Netflix, YouTube, and more. It can also play video and audio files you have downloaded on the machine. The EyeTV Hybrid is a USB TV tuner that works with cable and over the air HDTV signals (antenna sold separately).
The new version that just came out can also receive FM radio. It comes with the EyeTV DVR software too. It retails for $150.
I am not sure about your Logitech diNovo keyboard, as they make a separate Mac Edition too. The Revolution MX mouse works great on the Mac, it's what I use. Instead of Logitech's crappy drivers, I like USB Overdrive.It lets you assign all the buttons and wheels to whatever you like.
It is shareware that goes for $20. Your monitor will work without problems. The port on the Mini is a DVI, but comes with a VGA adapter in case you need that.
A new Mac will come with iLife, which has iPhoto in it. That should be sufficient for what you need. Although, Google just released Picasa for the Mac, in case you've used that before.
As far as Microsoft Office compatibility, the best would be Apple iWork. It includes Pages, Numbers, and Keynote. They are word processor/desktop publisher, spreadsheet, and presentation applications, respectively.
It retails for $79 and your new Mac should have a free trial on it. Another option is then open source suite OpenOffice.It's a full replacement for the MS Office suite and it's totally free. If you must stick with Microsoft, they do make Office for Mac 2008.
The home and student version includes Word, Excel, PowerPoint, and Entourage (Outlook replacement) and retails for $150. Your WD MyBook should work fine. I'm guessing that it's USB, so no problem there.
It's probably best if it's formatted to Fat32, as Windows machines can't read HFS+ natively and OSX can read but not write to NTFS file systems. With Fat32, either will be able to read and write. You will not run into any problems with the router, either plugged in through ethernet or over the air with wireless.
The free StuffIt Expander will work with your rar and zip files.So no need to worry about that. I believe that your iPod and iPhone must be formatted with HFS+ to work on a Mac (see link below). ITunes should help you out with this.
I would also recommend you get the Flip4Mac player and Perian. These will ensure that you are able to play most video types. If you're familiar with BitTorrent, you will want the new-to-Mac µTorrent.
As for the moment, that's all I can think of. Good luck!
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