If your Modem is the usual Dial-up type 56k modem that makes audible noises when you connect to the Internet.. then No. It will not be suitable for Broadband.
Also Broadband comes in different flavours; Cable from Cable TV type companies or the more common ADSL / SDSL type that use traditional copper phone lines.
I would suggest that you would probably be best obtaining their offered equipment, as they could troubleshoot any set-up problems you may encounter.
They appear to be offering you the option as you may already own your own suitable equipment, or indeed want say a wireless adsl modem/router for a home network for instance.
