No not all PSUs have PCI-E connectors, some have none, some have 1 6/8 pin and some have 4 or more.
When it comes to the PCI-E connector the best rule of thumb to have is if the PSU does not have the connector for your card, it was not designed to support it. Does not matter what wattage number is printed on the sticker because at the end of the day it could be just that.....nothing but ink on a sticker.
A quality PSU is designed to ouput its stated max load and has many safegaurds to prevent damaging the rest of the parts of your PC (poor quality PSUs have even caused house fires).
Never go cheap on the part that can destroy all the other parts.