Broadband is only a fast, always-on internet connection. For your pc, you will need a USB modem, which most broadband ISPs will provide free. You even connect these just like dial-up.
Because it is always connected to the internet there is a greater chance of some nasty person trying to interfere with your pc so you will need a measure of protection, normally a software firewall, an anti-virus program and an anti-spyware program. All are available free and the free versions are every bit as good, or better than, the commercial products.
The biggest debate is not usually whether to go broadband but which ISP to use.