Request the upgrade using 500s as early as possible, but some caveats to keep in mind. If you choose later to decline the upgrade because only one segment has cleared, there has to be Y availability to put you back into Coach. If coach is sold out, you have to take the upgrade or possibly bumped because they can't accomodate you.

The upgrade will trigger automatically at your respective window based on available inventory. UA is holding a lot of inventory for day of travel release. If that happens, you want to and don't want to check in until the last minute ... you'd want to check in early to get on the upgrade list, but once you check in, you need to have made your decision on the upgrade and asked UA to remove the request previously (or at the ticket counter).