If you decide that you're going to allow your child to venture forth into the World of Warcraft, the next step is to see if you have what is needed. It's probably obvious that they'll need a computer, an Internet connection and the WoW software. There are also a few things not mentioned on the boxed product that your child will/may need at some point. This section will get into all the items I found I used and that I know others used.
Blizzard did very well in this area. They want as many people to be able to play World of Warcraft as possible so the computer hardware requirements are modest by current standards. If (your or) your child's computer is able to play most recent game titles fairly well then it's likely that it will play WoW just as well. The official hardware requirements from Blizzard are available on their site. For the most part, what they list there is honestly sufficient to play the game with low to moderate graphics options selected. If you have any doubts about the ability of the computer in question to be able play World of Warcraft, browse to the Can You Run It web site from that machine. Let the site examine the computer to see if it has what it takes. Start typing "World of Warcraft" into the text box and choose whatever the latest expansion pack's name is after that. The site offers several ways to check your system and match it against the requirements. The method I chose will temporarily install a small application that scans the machine to see if it meets the minimum and recommended requirements.
Most people play WoW on desktop computers. Laptops can be used to play WoW, but they should have a discrete graphics chip (aka GPU) rather than an integrated graphics chip, which most do not have. An easy way to tell is that if the laptop mentions having with dedicated (or dedicated and shared) graphics memory, it almost certainly has a discrete graphics chip; if it mentions only shared memory for graphics, it is almost certainly using an integrated graphics chip. Some laptops are designed for playing games, and will do fine with WoW. I have played WoW on a fairly old, low-end laptop (with 2GB of RAM using Windows XP and with a dedicated graphics chip). With the graphics settings all set to low, the game played decently and still looked pretty good. In general, it's best to stick with a desktop machine.
The official requirements recommend 1 GB of RAM for XP and 2GB for Vista, Windows 7 and Windows 8. While it will run with those amounts, I would recommend doubling that amount in both cases to 2GB for XP and (3 or) 4GB for Vista, Windows 7 and above. When playing WoW, it's very handy to have other programs open like Internet Explorer or Firefox. That way, if one gets stuck or needs to look up an item, hitting ALT-Tab switches between the game and the browser. If you have only the recommended amount of memory, there may not be room for anything else once the game is loaded. One number on there that might be a bit low is the one for the amount of disk space needed, which Blizzard lists as 35 GB. That's a lot of disk space, but even so, the reality grows to much worse than that. However, as I mentioned above, Blizzard patches the game quite often. Some of those patches are hundreds of megabytes. On my computer, the folder into which WoW was installed had grown to over 40GB of space. That was a couple years ago, now, but they were advertising the requirement at that time as 25 GB. For newer computers with 500GB drives and up, this isn't a problem, but might be on an older PC with a smaller drive.
Blizzard offers the Blizzard Authenticator in the US, Canada, Australia, New Zealand and Latin America as one way to add a second level of security to your account. For $6.50, it's a steal. Blizzard also offers a free mobile authenticator application for Apple iOS and Android devices. Both add a good amount of protection to the account for very little or no money. This is the proverbial "no-brainer;" get one of them. It may take several weeks for the Blizzard Authenticator to arrive, but that should not be an issue. Account hackers aren't interested in the 1 gold, 57 silver that you or your child's level 12 character has or in the one or two rare items of armor they are wearing. Your child is relatively safe until they reach the higher levels where they have a large amount of gold and valuable items.
When your child reaches the point where they are doing instances (or right away if they are joining WoW with a group of friends), they will want to get a headset with a microphone. This is especially true in the higher levels or when and if they join a guild. The Ventrilo software, discussed below, is used to allow players to talk to each other over the Internet. It's much more efficient than typing messages into the party chat window (and doesn't require that the player stop playing in order to type messages). I do recommend getting a decent quality headset. A $10 headset sounds like a $10 headset to the other players who may not even be able to understand what your child is saying. Expect to pay more on the order of $20-$50. Make sure to get a stereo, not mono (single-ear) headset.
High-speed Internet Connection
This is one unyielding truism about World of Warcraft (and all online games, really): dial-up connections need not apply. Satellite Internet connections need not apply either because their inherent latency (the time for data to travel up to the satellite and back down to the earth to a hardwired receiver) is just too high for gaming. Wireless broadband (actual wide-area coverage wireless broadband as opposed to the wireless Internet inside a house or building) may work depending on the contention and speed in your local area. Just having a high-speed Internet connection alone is not sufficient. It has to be a continuous and reliable connection as well.
A case in point: one of my guild members had cable Internet service with an advertised speed of 8+Mbps incoming/down to his house and 512Kbps outgoing/up from his house. Theoretically, that is more than enough bandwidth for the game. However, every few hours - almost like clockwork - his connection would drop for about 20 seconds, which had the effect of logging him out of the game. It was extremely annoying to him and everyone grouped with him in the game. As it turned out (with much investigating on his part), the culprit was the way the dynamic IP service was implemented by the cable company. With dynamic IP service, which is the most common type of Internet service offered to residences, the cable company assigns an IP address to their cable modem when it first connects and periodically thereafter. The IP address is how the cable modem (and through the modem, his computer) is located on the Internet. He discovered that this particular cable company assigned new IPs to the modem every three hours. Most services only change the IP addresses every one to three days.
The company's explanation for this was that they did so to combat residential users from offering game and file sharing servers. Since his IP address actually changed, his connections to WoW were dropped. Pleading with the cable company got him nowhere. His solution was to add DSL service - at a much slower speed of 768Kbps/384Kbps incoming/outgoing - with the local phone company for about $20/month. From that point forward, he rarely had interruptions even though the service was much slower. The DSL connection still used dynamic IP service, but the IP address renewal period was much longer and when the IP address was renewed, his DSL provider generally assigned him the same IP address for weeks at a time. He kept the cable Internet for the rest of the house, but used the DSL connection exclusively for playing WoW. Suffice it to say, if you have a high-speed connection, but it's not reliable or bogs down at particular times of the day, it may not be good enough for an enjoying online game-playing experience. If you don't even have a high-speed Internet connection: cable, DSL, FiOS or otherwise, playing WoW is not an option.