Hello Fuel Boy,
I haven't flown on a BA 777, but according to seatguru dot com seats 21 J & K are good ones in World Traveller Plus class -- bulkhead aisle and window seats with extra legroom. You might have to put up with other people's kids though!
As for upgrading, I'm much more familiar with doing this on US airlines in the US, so this might not be helpful to you at all, and it might be rubbish advice no matter. Upgrading seems to be much harder to do these days then say 5 or 10 years ago and it is mostly a matter of luck. I've found that arriving early for check in and not looking too scruffy helps. If I'm not paying for an upgrade or using air miles, I usually make a
very polite request at check in, usually just asking if there might be a chance for an upgrade. This has worked on occasion. Sometimes I've been told at check in that I can't upgrade on my ticket, but I then make another, very polite request at the gate and have often got a different answer. It might be because at that point they are dealing with no-shows and are trying to shuffle seats. It's still a matter of luck though -- and don't make a pain of yourself, that certainly doesn't help!
I once asked if there was a chance of getting an empty seat next to me as I had a lot of work to do on the flight (which was actually true!) and they ended up upgrading me.
With the airline I fly most often, getting the request in early helps as they put it in a queue. I don't know what BA do.
Finally, I've found having a British accent in the US can do wonders for you, but unfortunately I doubt that'll have much of an effect on BA.
Good luck, and hope you enjoy Houston.
(Apologies for not posting the full URL above, but didn't want to fall foul of the spam rules while still new here - I have no association with seatguru, just found it a very useful site).