Whatever flight you might choose do pick one, at least 21 days ahead. At AA, upgrade requests put in for, 5-21 days incur a $50 fee and requests up to 5 days before the flight incur a $75 fee.

Also, do not limit yourself to the AA SWU, AA miles will do just fine. Both apply to the majority of fares published. AA, different from UA, makes no difference whether an upgrade is supported with an SWU or with miles.

Different from UA, at AA land there's no pre-reservation of SWU/miles at time of putting in a request for upgrade. You can put in your request right now, could be better for availability and definitely better to skip fees.