Assuming you take the PSU from the R-Pi shop, you should only need the following:
1) HDMI or DVI computer monitor, or a TV with HDMI or Composite input.
Aria currently have a basic 17" monitor with DVI for £57. Even better, it's *not* widescreen, that means more lines of code per screen for your money.
2) Cable to connect R-Pi to monitor. NB: many HDMI cables in shops are horribly overpriced, so shop around - Aria currently have one on special for £5.11.
In my case that will involve a HDMI-DVI adapter and a DVI KVM switch, sharing the monitor with other computers. Composite is a fallback position, the picture will be low-resolution and rather blurred with it.
3) SD or SDHC card to boot from - say 4GB or 8GB. Addtional storage for backups or bigger experiments can come later. You could also buy the pre-flashed card from R-Pi.
Some SDHC cards are definitely better than others with typical Linux filesystems - I suggest buying SanDisk for consistently good results. Other cards are usually designed only for cameras, whose performance needs are much simpler than a full computer. It's hard to tell which are good without prior experience, but Kingston (which unfortunately are all that Aria sell) tend to be particularly poor.
4) SDHC compatible card reader, to flash your choice of OS onto the card via your existing PC. These are often available bundled with SD cards, useful if money is tight. Otherwise £4.28 at Aria.
5) USB keyboard and/or mouse. Or PS/2 versions plus an adapter to USB.
In my case these are already connected to the KVM switch.
If you plan to do programming, strongly suggest an English layout (as opposed to, say, Nordic) as then the symbols are more accessible. Going upmarket (eg. Cherry) is also a good investment to save your fingers, but a basic £7.19 set is available from Aria.
Wireless versions are usually a lot more expensive than wired, so I would suggest a USB hub (under £10, Aria) before resorting to that. Depending on which distro you install, a mouse might not be necessary. In any case the Model B has two USB ports.
6) Optional: Ethernet cable and spare port on switch/hub/router. Cable may often be described as Cat5e and/or RJ45. A 2-metre cable is currently £2.71 at Aria.
It is probably actually more fun to try running it without Internet access, especially if you are trying to follow a programming course. Actually typing stuff in rather than just downloading it ensures that you read (and hopefully understand) the relevant code thoroughly.
7) A non-conducting surface to rest it on. Nick a tupperware lid from the kitchen, make a paper case, or just buy a spare mousemat. Also, try not to spill your coffee.
The key to knowledge is not to rely on people to teach you it.