While it is possible to build with a small PSU, it is wise to follow a process starting with the key components (CPU, motherboard, RAM) then to select the optional stuff like GPU if not included with CPU, CD/DVD drive(s), HDD(s), etc and lastly to consider how many USB devices might be added simultaneously (especially external HDDs). Once you have what you want, add up the power requirements and see if you have a comfortable fit. I would generally allow 33% extra power, especially as the smaller/cheaper PSU might experience sharp drops if the power required is close to PSU capability.
Do remember while specifying your new system, to take the time to confirm that CPU and RAM are both on the motherboard supported list on the manufacturer's website. Sometimes they specify GPUs too. It is easy to find that you have bought something which 'should' work, but doesn't.