Forgive the cheek of somebody who's only a couple of rungs up the ladder from you presuming to give advice, but sometimes advice from a fellow dinosaur is more valuable than from the nerds who want to plug their own needs.
It is my humble opinion that unless you want to play complex games or run massive graphics programs, the bottom-of-the-line entry level computer these days provides waaaaaay more grunt than you will ever need for what you say you are after.
Entry level specs are around 256Mb RAM, 40Gb hard drive, and somewhere in the high 2Gb processor speed. (The likes of you and I will NEVER be able to tell the difference between Pentium and Athlon.) For basic processes, this is ludicrously over-equipped and has happened only because computer manufacturers persist in pushing the fallacy that you must have the latest or be out of date. This is the only way they can sell new computers.
The last thing they want is for people to realise their current computers are good for five years or more, so they keep issuing more complex software which requires more space, memory and speed to operate, but doesn't do any more than what you've got.
I have a 900 Celeron which does everything I could possibly want it to do. Internet speed has buggarall to do with processor speed and everything to do with your ISP. You will be able to store thousands of mp3's on your entry level hard drive.
Get an entry level clone from a reputable dealer, option it to your specs and be amazed at what it can do.
*dons flak jacket to cope with incoming from the nerds*