Flying BA LHR->LAS later this week - should I check in right at T-24 or wait? Any upgrade tips?

I’m flying BA275 from Heathrow (T5) to Las Vegas this Thursday (30 Oct) in World Traveller (O fare). I’ve got BA Blue status (585 tier points), so basically low-tier but not completely new.

I haven’t checked in or paid for a seat yet, right now only aisle seats are available for a fee, and I don’t really mind where I sit. My main question is:

Should I check in exactly at the 24-hour mark to grab a free seat and lock it in? Or is there any point in waiting, like maybe getting a better chance at a bump to World Traveller Plus or Club if economy’s oversold?

For those that have gotten an upgrade, did you get it at the check in desk or was it online? Never had a long haul flight with BA or gotten a bump before.

Thanks in advance