Every electronic device you buy these days seems to want to have internet connectivity. That's good, but how do you achieve this connectivity in all parts of your living areas? There's a multitude of choices (along with acronyms and technical jargon) which make it difficult to decide how to build your network and be satisfied that you've achieved your optimum solution.
Connection to an Internet Service Provider (ISP)
NBN Note: The "nbn" company acts as the provider of the physical infrastructure to your premises and as the wholesaler of internet connectivity to ISPs (retailers). Although nbn may initially liaise with you to install the physical connection, after that your interactions will generally only be with your chosen ISP. Getting new NBN connectivity to your premises (whatever the underlying physical infrastructure may be) gives the opportunity to review who your retail ISP will be. eg. Telstra, Optus, TPG, iiNet.
If you have a telephone landline into your premises then you're probably, but not always, going to be able to get a broadband "DSL" connection. Depending on how far you are from your exchange and what equipment has been deployed at that exchange will determine what type of DSL is available and what bandwidth (speed) can be realistically achieved. To a certain degree that equipment may also restrict your choice of ISP.
If your house has a cable connection to the Foxtel/Optus optical lines then you have the option of subscribing to one of those providers as your ISP. Cable connections are high speed but the bandwidth is shared with your neighbours so can be variable.
If you're able to get a 3G signal on your mobile phone from your home then you also have the potential to use that as the feed for your home network. Typically these connections will be slower and more expensive than DSL but because they use less physical infrastructure to get to your location they can be a great option when DSL isn't available. The Telstra "4G" product is a souped up version of 3G which can achieve very good speeds if you're in the appropriate coverage area (usually metro).
WiMax is a different wireless method of getting you connected. In general this is only available in the "metro" areas due to the cost for the provider to deploy specific infrastructure. If you're in the right area this will generally be a better bandwidth option than 3G.
The Modem / Router
Modem: Whatever method you are using to connect to an ISP, the connection point in your house has to convert the signal to something that all your devices can read - that something is the modem. So your ISP (or NBN) will provide, or recommend, a modem which will then give you one or several options for your devices to connect to.
Router: In almost all cases these days the modem will also include the functionality of a router. The router allows you to have multiple devices that can independently use your single connection and it makes sure that any info that comes in is routed to the correct device. The router will allocate an IP address to each device that connects to it.
Firewall: By default your router will probably be creating a small private network within your home. The great thing about this is that it means that you're automatically protected from a significant proportion of the "nasties" out there because the IP address associated with each of the devices in your house is private and inaccessible from the other side of the router. This is basic firewall functionality. Almost certainly the modem/router/firewall will have many other options to both lock down your connection and in certain circumstances open it up to "friendly" traffic.
Connecting Your Devices
Ethernet Cable: If you want to connect a device that sits permanently somewhere near your router then an ethernet cable strung from the router is the best option. Most routers these days will have 4 ethernet sockets available. If you're lucky enough to have a house with ethernet wall sockets installed then you should be able to plug a cable between the router and one wall socket and another device into any other socket. Modern devices have "auto-detect" to make sure they all use the same protocol and speed when they talk over ethernet so you should be able to just plug and go.
Wireless: Your mobile devices almost by definition will want to connect to the internet wirelessly and certainly all of Apple's devices come with 802.11 capability built in. The wireless network is created by a "base station" or "wireless access point" (WAP). Many models of modem/router also include WAP functionality. The Apple Airport devices are WAPs.
Turning on the security on your wireless network is very important if there is any chance of somebody else getting within a few hundred metres of your place - the wireless signal won't stop at the walls. Modern devices will all offer the WPA2 method of encrypting your wireless traffic and, at present, this is the best method available.
There are unfortunately configuration settings that may need to be altered in the WAP to make sure the wireless signal is acceptable in all parts of your home. In large properties, or places with bad interference, you may even need to deploy multiple wireless "base stations".
Ethernet Over Power: This is a really good middle ground between the consistency of ethernet connection and portability of wireless. EOP devices allow you to turn every power socket in your house into an ethernet socket. Plug one EOP module into a socket near your router and connect the router and module with a short length of ethernet cable and then plug another module into a power socket near where you want to deploy your device. eg. a printer. Run another short length of ethernet cable between that module and the device and then both the router and the device will think they are simply connected by ethernet cable. The quality of electrical wiring connections will impact the data connection quality so it is recommended to plug these dives into a wall socket rather than a power board or extension lead.
It is qute possible that you may be best served by a combination of these connection methods. As mentioned above I can help you work out what is optimal for your situation.