Hi,
A QUICK format does NOT scan for bad sectors, whereas a FULL format does. So, you can think of it this way:
QUICK Format + CHKDSK /F = FULL Format
If you are confident that your SMART assesment tells you you have no bad sectors, then a QUICK format is probably sufficient. If it was me, and I was doing a completely new installation on a previously used HDD, then personal I would run a FULL Format, regardless of what my SMART assesment would look like. A FULL format takes considerably longer than a QUICK format, but you get the satisfaction of knowing the status of those clusters.
Regards,
Golden