When you say modem do you mean a cable or DSL modem?
They provide the interface to a PC from your ISP. Should you want to allow more than a single PC to have access to the internet you would need a router.
As for a risk of connecting to the internet through your modem, you should verify the Firewall is enabled in your OS. Also, you could try downloading Zonealarm (free download). This would provide you with some protection.
Just my 2 cents ....