Every home needs a network these days and most have a connection to the internet. Although many ISPs provide a free modem sometimes they are not as reliable or stable as you would like. Upgrading to your own router is a good idea and I have found the best to be the Apple AirPort Extreme or Time Capsule units. These have gigabit ethernet ports and dual band wireless radios included to get the best range and speed. Of course if you are an ADSL user rather than cable you will also need an ADSL modem (Zoom 5715 or Draytek Vigor 120) to be able to get to the Internet. Although this may seem expensive it is the best solution for your home network needs. You can even use them to extend your network range (bridge mode) if required.
Although in the UK many internet service providers (ISP) supply a router as part of the package it can be advantageous to buy your own router. (Sky do not allow the use of any other router apart from their own!)
A good option is something like the Netgear D6400 or TP-Link Archer VR900. These will even work with fibre optic broadband as they have a VDSL modem built in (to work with Virgin they still need the Virgin cable router but will take over the Wi-Fi duties). Their enhanced dust band Wi-Fi with beam forming technology will provide a better Wi-Fi environment, especially if you have lots of users in your household.
The Time Capsule is a great backup option for Mac users but more flexibility can be obtained by using a NAS (Network Attached Storage) device, such as the Synology DS212J (fitted with a pair of suitable 2TB disks). This can also be used with a Mac or PC for backup (also supporting Apple time Machine) but also works as a media server to stream your media to suitable devices (TV, Xbox 360, PS3 and AV receivers). Note any Windows PC that has a network disk needs separate backup software as the Windows Backup program will only work with local disks. A workaround is to use VHD (virtual hard disks) if you have Windows 7 but needs some work to enable auto mounting of the VHD. I would suggest you upgrade to Windows 8 or ideally buy a new Windows 8 machine as this will make life easier.