I refuse to pay the Mac tax. Windows boxes are pretty cheap at this point. Building your own is the most economical way to do it, but you may not want that option for any one of several good reasons. Any of the Intel i-series (i3/i5/i7) processors should be adequate for your needs. RAM is dirt cheap these days, so get 8GB minimum. You may be able to move drives over from the old box (depending on how it died), so you might save on storage.
Of course, in addition to the Windows and Mac options, there is always Linux, which will do more with less hardware than either of the other options, and is free to boot. If I were building a box to do the things you're describing, that's the way I'd go unless I needed OS-specific software.