For what you are talking about, you don't HAVE to have a new computer. They can always send you jpegs or PDFs of the work, which your computer should be able to view without any issues. That being said, if you need a new one, I'd try and get one that is as powerful as your budget would allow.
As for software, that is a hard one. There are two big contenders out there - Corel and Adobe, and there are a lot of opinions on which to get. I would only look into these if you are going to be editing files. Of course, it would be easier for you to look at the same software your designer is using.
As for what I use, Macs at home and work, as well as PCs.