Yeah the modem that my buddy gave me (which was a real modem) was also a PCI modem by USRobotics. It worked pretty well for me. You will have to look into whether or not your modem is a real modem or not, though (or if you give me like a week I can look it up - I am pretty busy recently). Almost any distribution of Linux you try will either come with a much newer version of OpenOffice or will have it available in their repositories for installation after you install the OS itself. I am not to sure about your printer, maybe Linux_0 could tell you more about it? As for pdf readers, there are a TON of them. I like evince pdf reader, but GGV is also pretty good. If you need to continue using windows for whatever reason, I suggest you ditch Acrobat and go with Foxit as it is a LOT more lightweight (i.e. consumes fewer resources). As for burning CDs/DVDs, Brasero and especially K3b are about 10^9 times better than Nero. And this statement is coming from an ex Nero user. It actually got to the point where I would reboot into Linux anytime I wanted to burn something because Nero would give me problems and I have only had CD burns fail maybe twice in the two years I've used K3b. As for your Bible study program and DVD shrink, they may be able to work using either WINE or Crossover Linux. The former is always freely available and can be installed from your distributions repository. The latter normally costs about $50 but is being distributed for free by the creators today only (10/28/2008) until midnight Central Standard time, so if you want a copy of that I suggest you connect to http://down.codeweavers.com/ , give them your email to get a free serial number, and then click on the "Crossover Linux Pro" link to get a free copy of this program. Basically those two programs are programs that allow you to run windows applications under Linux, so they may come in handy for you.
By the way, if you don't like internet explorer 6, you should try Firefox or Opera Browser. They both are available under Linux and windows for free. As for a windows media player replacement, I like audacious media player to play my music and I use mplayer to play my videos. Audacious is similar to winamp except it doesn't play videos. Mplayer can play videos and music but it is better suited for video playback. If you want a program that does both, VLC is a good option. If you want a program that will help you organize all your music and play it, then you should try Amarok. There are probably a good 10 or 15 programs (maybe more) that all accomplish what windows media player does, so try them out and see which ones you like.
Finally, whether you use NetZero or a different dialup provider (as long as it isn't AOL), it shouldn't matter. You should just be able to use the built-in dialup connection program that comes with your distribution to connect (without having to install any special NetZero software). The reason why I say not AOL is because I think they require you to connect to their system directly and use their browser and things are weird if you don't, but I may be wrong.
Hope this all helps!
-Zorak