Memory or RAM
RAM is something that you do not want to skimp on. I told you above to choose a slower processor, but with RAM you want as much as you can get. RAM is your computer's temporary memory, think of it like your desk space. The larger your desk is the more you can work on simultaneously. If you run out of desk space you'll need to be shuffling papers around a lot and that will take time. Your computer is the same way, without enough RAM it will use your much slower hard drive for temporary storage and that will cause a huge performance hit.
RAM is also very cheap right now, so it doesn't hurt to buy more. However a computer manufacturer will often charge you more than you deserve for more RAM, so I recommend buying the minimum amount of RAM and then buying extra at another store and installing it yourself. Installing RAM isn't as hard as you think, you literally cannot put it in backwards so it's hard to mess things up. Installing it yourself could save you $50 or so, so it's definitely worth looking into. The only caveat for this is that you can't mix and match RAM, all of your RAM must be of the same type so when ordering or buying your new chip make sure you know what type of RAM you have. The brand name isn't important, it is the actual type such as "PC133 SDRAM." Sometimes though manufacturer installed ram is cheaper than retail store bought stuff so do price comparisons before purchasing your PC so you know how much the upgrades will cost you if you do them yourself.
There are also different types of RAM, SDRAM, RDRAM, DDR SDRAM. Some RAM is faster than other RAM and so it performs better. For WPIE you do not need fast RAM and SDRAM, which is now the slowest, should be good enough for you. However most new computers are coming with DDR RAM now, which is much faster, so this choice will likely be taken out of your hands. Still though if you have the option choose the cheapest one.
The minimum amount of RAM you should have is 256mb, ideally you'd want as much as 512mb if you can afford it.
Hard Drives
Hard drives are your computer's permanent storage. How large of a hard drive you have dictates how many MP3s you can have, or how many hours of digital video you can store. A hard drive of 40gb should be sufficient for a WPIE user, even one with MP3s, but if you have a lot of MP3s (think thousands) and even small amounts of digital video you'll want more. A 60 or 80gb hard drive should be enough for just about anyone who doesn't do digital video or otherwise store a large number of picture or music files.
There are also different hard drive speeds, 5400 is the slowest, but you can find them up to 15000 RPMs. A faster hard drive is nice if you have large files that you frequently load or if you do CD burning, 15000 would be overkill for most people though, 7200 should be fine for most.
Video Cards
Video Cards are very important for gamers, and also for people who do digital video or who want to watch DVDs on their PC. If you're not one of these people a cheap 64mb video card will be enough. If there is a gamer in the family ask him or her what they want, they'll probably know. If you're shopping for a higher end video card I recommend ATI Radeon cards. They are the best price/performance ratio.
Sound Cards
A cheap sound card (whatever is the cheapest available) is really all most people need, it will sound good enough for playing your music and that's about all you'll need it for. People who are really into games or into mixing their own music may want something better. In other words, whatever they give you is fine and don't buy the upgrades.
Network Cards and Modems
Nearly all new computers now come with both a modem and a network card so there isn't much to say here. The only real issue you will need to ask yourself is if you want a wireless network or a wired network. Basically if you have broadband Cable or DSL do you want to have to run a cable from your cable outlet or phone jack to your computer(s), or do you want to do it wireless? It will simply depend on your home setup. If you go the wireless route you should get 802.11b wireless equipment. You shouldn't automatically buy a bundle with your PC though. Do your homework first and shop around. It may be cheaper to buy it seperately.
Peripheral Equipment
These items are mostly just dependent on personal preference. The only thing I can say is do not waste your money on a "multimedia" keyboard with "quick access" buttons, you won't use them. I'd also recommend an optical mouse as they are nicer and last longer. This is also where you can make up for choosing the cheapest processor, ram, and sound card and buy yourself a nice LCD monitor. LCDs, in addition to saving desk space, are easier on the eyes because they do not flicker.
One other thing to watch out for is when buying a printer look at cartridge cost. Some printers are cheap, around $50, but their cartridges can be $30. I highly recommend getting an ink-jet refill kit, you'll save bunches. Also I recommend Canon printers as they are dependable and do not overcharge for ink.
Things Not to Buy
Do not buy zip drives or any other removable media drive, CD burners are cheaper and better if you want to remove large files. With today's burners it takes a minute or two to burn 700mb of data. Such drives are now dated and mostly unused.
Do not pay for extra software such as MP3 playing software that you can get for free. Using a site like downloads.com will give you access to plenty of freeware programs that the computer manufacturer might try charging you for. Also Windows now comes with most common utilities.
In most cases you will not want to buy any extras like removable media, or even digital cameras, from your computer manufacturer as part of a package deal. You'll be able to find the same items for less elsewhere.