As for time of day - I have never had much problem except late at night with selection. You can always call first to make sure they have a few available. Are you doing an off-airport location? If not you might consider it as most airport locations charge an extra tax that is different for people who have flown within the last 24 hours as opposed to people who are local.
After you make the reservation and have a National confirmation number you should be able to call or go to their site and amend your reservation to include the number. I actually got a room from Hotwire that turned out to be a Westin and was able to go put my Starwood number in the following business day.