The choke really doesn't matter with US style "trap." You will get to shoot while the bird is within 30-40 yards if you don't pooch it.
Handicap it might make a bit of difference, especially if you are slower in the reflexes, more choke will be better to a point. At the 18 yard mark, you will likely be breaking the targets just inside 50 yards. Modified isn't bad.
International style trap, now there is a game. Less than 7/8 oz shot, start from low gun position at handicap distances, with the targets moving faster. Here you need full choke.
Shooting with more constriction will make you have to be more on the bird at short range. If you hit, you will get a greasy cloud of smoke. As you get further out, the pattern disperses more, and if you shoot a less constricted choke, you will likely have holes in your pattern. Murphy's law will make sure that target is in the hole.
To reliably break the target you need to hit it with 3-4 pellets. Not too hard to do with the right pattern density, if its in the pattern in the first place.
Patterning is something every shotgunner should do a couple times. But it requires some basic statistics and is awfully boring if you want to do it right. When I had pretensions of being competitive, I did this with 10 shots of every load with each choke at 5 yard intervals until the pattern density was less than 50% for a 36" circle (30 is ideal, but I had a yardstick, and that is what I used, by god...) Coincidentally, by doing that I learned real well that inconsistencies in gun mount change your POI substantially....
All this is if you worry about finding the right load. If you are just out for fun, get a box of wally world and whatever gun you have and make up whatever excuses you want (gravitational variation always works for me....)