I’d warmly recommend the setup and I’m sure the hd5770 will work without problems.
Nvidia has had a history of better drivers, but the new ati drivers are really good too, and just because the drivers have been good/bad before doesn’t necessarily dictate what they will be like in the future. Companies change and priorities change.
Anyway if you can spare som extra bucks, the nvidia gtx460 has the best performance to price ratio right now. It also has a very high performance to power ratio.
Being a custom computer builder myself I wouldn’t buy any pre-assembled computer, especially not a refurbished one, unless it’s really cheap for its specs. It’s a bit risky and usually comes with a few surprises.