Some good choices you can consider are Mandrake, Suse, Fedora or Ubuntu. Personally I favour mandrake among these, but then again, opinions vary.
If your modem does not support linux, and no unofficial drivers have been written for it, it won't work for sure under linux. But have a dekko at
www.linmodems.org ,
www.linuxant.com and your modem company's site. If unsuccesful, try mailing the company with a request to make drivers for non-windows platforms.
For installing linux, as sreevirus said you will need a seperate partition, if there is no unpartitioned space left on the disk, use a tool like Ranish Partition Manager or the commercial tools like Paragon partition manager etc to resise your existing partition. Some distributions (like SUSE?) can automatically resize your partitons for you.
Step by step instructions vary from distributions, so check their official site for info
