To pick up on a few points (with 450,000 airmiles in the bag...)
To get to Silver tier with BA requires 600 tier points. This gives you lounge access, and more chance of an upgrade. However, a transatlantic return only gives you 120 points, therefore you would need 5 return trips in a membership year to hit this. At the end of the membership year, your balance is zeroed, and you have to requalify. Flying Worl Traveller Plus, Club, or First gives an override on the tier points, 240 points in Club for an "across the pond".
Once you have hit Silver, your membership year is restarted, and tier points balance is zeroed. You then have that year to gain a further 1500 points to make Gold. Obviously that is rather a lot of crossing the pond activity. If you make it, BA treat you very well indeed, because they will have taken a huge amount of income. Personal experience is that once Gold, I was ALWAYS upgraded to Club, and this year, despite only having 585 points (i.e. not even enough to requalify at Silver), I was renewed at Gold. Cabin Service Director, and sometimes the Captain, would come and introduce themselves on every flight, a minor point, but a form of recognition.
As for airmiles, basically one mile flown=1 BA mile. So across the pond and back in Economy gains approx 8-9000 miles. Higher cabins and tier levels gain multipliers, so a Club return as a Gold member would gain approx 36,000 miles. To spend the miles, a transatlantic return is 50,000 miles.
I now live in the US, so I don't fly BA any more, it's Delta. Their scheme is pale shadow of the BA one, BUT, the miles are transferrable, and indeed saleable or donatable.
I've sat next to many a Civil Serpent across the pond on BA, and they all had their Silver cards....