If you are a "high-mileage" flyer, as you say, then you will receive free upgrades on domestic flights. You will also receive a number of certificates to upgrade international flights. Note you don't say where you live, so I will assume the USA, although many other airlines have similar upgrade schemes.

There is no way to get upgraded all the time. The higher your status is, the better your chances. The only way a credit card would help is if you spend so much (99.999% of such cases will be business cards) that you spend the earned miles on upgrades.

I have no idea where you live, but I would recommend US (if you're in the USA. They've got sort of a bad reputation, which means many frequent flyers are elsewhere. You can get free domestic upgrades, and as a Silver, the lowest US status, I was upgraded on 4/5 domestic degments this year. You can pay $200 for a "trial" of their status, and that way you don't have to earn it. You just have to fly 7,500 miles in 90 days, so if you do this before a TATL trip, it will be knocked out with only 1 trip. Then just sit back and enjoy the free upgrades.

And welcome to FT!