It's really hard to say. Good, brand-name power supplies are a lot better at providing consistent power than the cheap ones that are included with most PC cases. The cheap PSUs tend to be rated at the peak power that they are able to provide, while the brand names tend to be rated at the sustained level of power. So if you have a good 250 watt PSU, you might be able to get by where you otherwise would need a 300 watt PSU.
You problem is complicated by adding additional components besides what would be found in a bog-standard PC. If you google the term "power supply calculator" you'll come up with quite a few hits that can help you determine what it is you will need.