On Delta, nearly every time I've booked a flight in the last couple of years, I've gotten the pop up that says "for X dollars more, you can be in first class." And, if it's reasonable, I take them up on it. For our March trip, I booked in August, I think (which is a LONG time before). The flight was nearly empty when I booked, and the first class cabin was completely empty. That's your best shot for a decent price upgrade. If all the seats in coach are gone (or nearly so), the price to upgrade becomes steeper. If there are only a couple seats left in first, the price becomes steeper. The difference I paid between coach and first class for a 4+ hour flight was a bit over $100 each way. The coach seats are now selling at a premium for my flights since they are nearly sold out....so the coach fare is over what I paid. And, first class is now 4X the cost of what I paid (which is totally not worth it). But, for $100? Sure. To me. I get 2 bags (limit 70 pounds, rather than 50) checked for free (and we bring a lot of water sport equipment with us, so we use it), a free meal each direction, and free drinks (including the ever so important pre departure beverage....LOL), and MORE room. I am tall, with very long legs so coach is just extremely uncomfortable for me these days as the pitch has gotten smaller and smaller back there. I can do it for a couple of hours, but more than that it gets bad. So, I upgrade when I can.
YMMV. United is another one with decent FCM. American, not so much, IME.
Note that I have "status" in no airline at all. People with status get even better $$$ offers than I get. I'm a "member" of the Delta frequent flyer program, but since all my travel is leisure based these days, not enough miles to even get "lowly" status.
The one place you DON'T get good upgrades offer is in international business class, or cross country if you are talking a plane with lie flat seats. They will completely gouge you for that. I'm looking to take another Asia trip in the next few years, and OMG the cost of business class is just through the roof on most airlines. Sigh. I'm going to have to save my $$$. Last time I went, it was in coach, and never again. I'm too old for a 12+ hour flight in coach.