buy Business fare or wait to upgrade at checkout or airport checkin (day of flight)?
 

I'm wondering if there's any better strategy to go ahead and book a coach one-way ticket and then either pay for an upgrade to business class at checkout if I see the flight is very full (and might not get an empty seat next to me) or take the chance that I'll get prompted to buy an upgrade at the airport on the day of the flight or when I checkin 24 hours before?

Thanks!

Okay I'm assuming you don't have elite status/stickers/miles currently with AA.

An upgrade at check-in 24 hours before is not guaranteed and I wouldn't do it unless you are familiar with the route despite the fact that it may be cheaper than booking business outright. See LBFU thread.

It all comes down to, are the marginal benefits of sitting in business class worth the extra price to you? Upgrades 24 hours prior (LBFU) are definitely cheaper ($45/500 mile segment) than buying business outright most of the time, but you pay for that difference in price on the off chance that an upgrade is not offered.

Load Factor Based Upgrades from coach to business for international flights are incredibly rare (in my experience). If you're willing to pay for a confirmed seat in business go for it. You'll get the mileage/EQP bonuses as well.