Don’t let some idiot at a big box store try to upsell you too much gigi. For your needs, literally any desktop computer being sold as new will fit your needs. You could go down to Wal-Mart right now and buy the cheapest computer on the shelf and it would be just fine for Microsoft Office type applications and playing music. If I were you, I’d try to find a good package deal with the computer and monitor and possibly an included printer for somewhere in the $500 range.
Windows XP or Vista (all computer come with one or the other - most have Vista) both have Windows Media Player included which allows you to “rip” or copy CDs to MP3 format on your computer. Then it’s as simple as copying and pasting your music from your music folder to your iPod folder.
If you have a lot (and I mean a lot) of music you want to copy to your computer, hard drive size is important. The average song when converted to mp3 is about 4 megabytes. There are a thousand megabytes in a gigybyte, so a 100gb hard drive would hold about 250,000 songs. Of course, there will be other things on your hard drive which will occupy a bit of this space - Windows, pictures, games, applications, etc. I would recommend getting a computer with at least a 150gb hard drive. You’ll find that when you actually own a computer, you’ll start using it for things you never thought you would and this can take a lot of space. For example, the gaming world’s biggest addiction, World of Warcraft, uses 12gb of space.
Also, check to make sure your computer comes with a 56k modem. Most computers still do, but I’m not sure if this is universal. If you decide to upgrade to broadband, any modern computer already has the hardware called an ethernet card (except for the modem, which your broadband provider will provide you). In the case of a cable modem, a wire runs from your cable jack to the modem. Another cable runs from the cable modem to your ethernet card.
As far as dial up internet goes, it’ll run you somewhere in the area of $10-$20 a month. You’ll run a phone cord from the 56k modem in your computer to your phone jack. No special hardware is required. As others have said, dial up internet sucks. it ties up a phone line, is unreliable, and sloooooooow. Broadband internet will probably run anywhere from $30 - $100 a month depending on location, your provider, and speed. Unless you’re a very casual internet user (checking your email and horoscope twice a day), you want broadband internet. It’s especially worth it if you want to watch videos and listen to internet radio or do multiplayer gaming. While dial up may satisfy you at first, you will end up finding a reason to get broadband.
If you find a computer you like and keep the money you have from burning a hole in your pocket, report back with the brand and model number and we’ll let you know if it’s a good deal or not. Good luck!
Edit: Crap. I need to stop fixing something to eat halfway into my post. I will get beat every time 
