will 300W branded (hec or seasonic) PSU be sufficient for computer with
core i3 processor (and its on-processor GPU)?
will it still work without problems even with basic GPU?
A 300 watt PSU will be more then enough to run that on onboard graphics. And depending on your GPU it can still work go to the link in my sig for more info and if you still have a question feel free to ask here or there.