A couple of comments on 'myspark's comments:
"Replacing an 8 year-old router will not increase your bandwidth. Bandwidth is what you've signed for with your ISP."
Sometimes replacing your old router does improve your bandwidth-- you just have to agree to pay your ISP more each month. They will either send you a new modem (usually with a built-in router), or give you a list of approved devices you can choose from. I think my ISP would let me use a faster modem, but wouldn't let it use the higher speed unless I offered them more money!
If you have a separate router (that's the section with multiple jacks to plug in ethernet cables, or that runs the in-house WiFi connection), it has to be at least as fast as the modem, or you don't gain anything.
re: the start of the connection talking...
The modems talk (with my cable modem there's no speaker, so you can't hear it talking to the modem at the ISP) to agree that both ends can talk at a certain speed: "do you understand me if I talk this fast?" >yes< "How 'bout now?" >yes.< They do this until one end or the other can't be understood at a higher speed.
Unfortunately, in my experience the ISP doesn't care if a file can be downloaded in a timely manner-- if you want to download a Windows update over a dial-up connection, no problem from the ISP!
And if the file fills up your hard drive, oh well...