Any Linux OS can be as dial-up friendly as any other, provided the necessary software and drivers are installed or included. Such software would be pppd, the PPP daemon, and for example wvdial, a command-line dialer, and/or maybe if the Linux was running a KDE desktop, you might like to use KPPP as a GUI dialer.
Ubuntu or Puppy or Mint might be good Linuxes to try out, if this will be your first Linux OS, but other members will surely suggest some other ones too; it's a matter of preference really.
The real important question will be: What sort of modem do you have? Can you tell us what is the make & model of the modem? As much detail as possible will help, such as, is it a PCI modem, or a USB device? Can you point us to a website that shows us the modem and its specifications?
Best regards, and welcome to LQ