2) Modem. A bit like filters, you pays your money, and takes your chances...
Some ISPs provide their own routers - SKY and BT (HomeHub) being obvious examples. These are then quite locked down - which is not great

They
can be hacked, but that's a bit beyond what I'm explaining here!
However, if you're with a generic ISP, using your own USB modem, then do yourself a favour and splash £50 - £70 on a decnt one. Netgear's DG834GT, Billion BiPac 7300G, or an unlocked 2700hgv are considered dog's bits
These modems all connect to your PC via wireless or ethernet (network cable), so you will need to make sure your PC can do this.
The main advantages are:
You can then share your b/band connection with other PCs / xboxs / PS2/3/Ps etc in your house
And these modems are able to cope with low SNRs without dropping the line - more on that in a minute
