We were able to buy our replacement desktop about a year ago for around $500. That price included a 19" flat screen monitor (both computer and monitor were on sale separately).
I really depends on what you plan to do with it. I would recommend a big hard drive (I suspect you'll be taking lots of pics of the little one to come!). Photos and mp3s can take up a lot of space. Our computer has a 160 GB hard drive, for instance. Most new processors are going to be fast enough for you. It'll also come DSL ready, so that's not a problem. Make sure it has at least 1 GB (preferably 2 GB) of RAM if you are going to run Vista. And make sure that you get Vista Home Premium (as opposed to Home Basic).
If you are just going to surf the net, type and print documents, load pictures, download mp3s, visit the Puritan Board (

), etc., it doesn't have to be a super machine. The thing will be obsolete in a few months anyway. I would watch the sale papers and see what the major retailers are offering. We bought an ACER (a cheap brand) and are happy with it. A website you can check is
C/Net; they give good product reviews and can tell you more about what specs to look for on a new computer.
I'm assuming, of course, you aren't a Mac person!