Here is a nice tool to help you find out what you need is a PSU http://extreme.outervision.com/psucalculatorlite.jsp
Personlly I would not match a 350w PSU with an Intel® Core™ i5 processor and a higher end video card in the HD7850. The problem is that this build needs about a minimum of 300w without any extra case fans or HDDs. Now since a poor quality PSU may not even provide 75% of the rated wattage it is very likely that a 350w isn't going to be able to power your components to the level that they should.
I generally match an Intel Core i5 and a higher end video card up with a PSU in the 500w to 600w range.