Welcome to Linux (or open source) world,
If your Linux have the modem driver, then you can connect internet easily.
Probably using this command in terminal:
but I don't know how your modem will work. Are you use usb, RS232 or built in modem?
About the wine, you can go to http://www.winehq.com
to see the wine supported application 1st before you try some application which we know DON'T WORK.