One thing I suggest (especially since you have dialup) is to get a Distro that has the newest versions of programs bundled with it. It's will annoy you if 90% of the programs bundled with your distro are not so new.
That's what I have experienced with debian. I love debian now that I have most things perfect, but the programs packaged with it are not new enough and a lot of them are useless to me because of that.
You probably don't want to be uninstalling old versions, downloading sources of new versions and compiling right away just to get things up to recent versions.
You should read this.
http://www.hardforum.com/showthread.php?threadid=567412
From what I've heard, suse 9.0 is the best for begginers, but I can't say personally. It comes with KDE 3.1.4 and GNOME 2.2 Desktops , where the newest version of debian only comes with kde2.2.2
You also might want to see which if any versions have the 2.6 kernel so you don't have to download and compile it right away if you want the newest kernel. Suse 9.0 has a test version of 2.6.
However, messing with all that stuff is the fun part.
People rave about fedora core, gentoo and slackware.
Debian is great and will force you to learn more.
Of course most packages programs I find on the net are in red hat's package format.
You should also really research on which has the most programs that you would use.
There are a few updates for programs that will take a little time to get into distros, so you might want to consider waiting for a little bit because you don't want to have to download a million updates with dialup.
You'll also want to make sure you have a compatible printer so you don't have to use special software to print. You'll also want to make sure you have an external serial hardware dialup modem (most are hardware) or an internal hardware modem. (Very few winmodems work in linux and the ones that do might need special drivers). A lot of people have trouble getting non-generic video drivers working for ati cards, so you might want to consider that.
Researching what distros have bundled drivers for the devices you have will help too. Make sure you have a sound card that will work without downloading and compiling some hard to find drivers.