Monitor: Viewsonic VX2239WM. The beauty of this inexpensive monitor is that it has the same resolution and aspect ratio as a 1080p HD TV, as well as both HDMI and DVI inputs. So, you can plug in a Blu-Ray player, your HD cable or satellite player, a Playstation 3, or an Xbox 360 at the same time as your desktop computer, and switch between them with the press of a button.
Keyboard: Logitech Internet 350 Keyboard. I have a fairly high typing speed, and am picky about keyboards. This inexpensive but durable model has a solid feel, with just the right amount of spring to the keys. No strange layout, no strange shape.
Mouse: Logitech M500. Corded, with laser technology at a reasonable price.
External Hard Drive: Western Digital Elements 2TB USB 2.0. At present, for maximum compatibility, I recommend sticking with 2TB as the maximum drive size.
Printer: Brother MFC-8480DN. It prints, copies, scans (including legal-sized pages), and faxes. The duplexing works beautifully: I think I've only had it jam once or twice, despite the fact that I've printed many thousands of pages on mine. When you replace the toner cartridge, I recommend replacing it with the Brother High Yield TN650 model. [Note: If you need your printer to connect to your home network wirelessly, rather than through an ethernet connection, then get the (otherwise identical) Brother MFC-8890DW model instead.]
Speakers: Klipsch ProMedia 2.1 Computer Speakers. Great sound at a reasonable price. It has an aux input as well as a headphone output, so you can get a 3.5mm audio cable and connect the audio output on the above monitor to the speakers: that way you don't have to unplug anything when you're watching whatever you plugged into your monitor via its HDMI input.
Headphones: Sony MDR-ZX100. Comfortable, decent sound, inexpensive. Uses a regular audio plug, so you can use it with either your speakers or your portable music player.
Game Device: Xbox 360 gaming console. I've come around to the viewpoint that most people are better off with console gaming, rather than trying to game on their desktop machine: you'll never be pressured to upgrade the video card or memory for the sake of a new release, you gain the ability to rent games (e.g. at Blockbuster) rather than buying, you gain access to a unified mechanism for inexpensive casual games, and the number of technical frustrations you experience drops down basically to zero. You'll need to pick up an HDMI cable, which is necessary but not included.
As far as the desktop computer itself goes, now that it has been relieved of gaming duties literally the only requirement is that its video card be able to output at the monitor's native resolution (i.e. 1920x1080) via a DVI output, and that it have enough RAM and a powerful enough CPU to run your preferred operating system smoothly.