For 16 yard trap, Remington's Modified is just fine (Browning's Modified is a bit more open, at least mine is).
The advantage of a tight choke for trap is that you can see where you're hitting more easily, e.g. if you break the left half of the bird, you can actually tell by watching. This helps you make fine adjustments to your shooting.
However, at 16, you can do that with a Modified. Farther back, you'll have a hard time doing it.
Remington's chokes are cheap. Grab a Full choke if you see one at Wally World or something, or just get their "upgrade kit" that includes IC and Full choke tubes, a nicer (faster) choke wrench, and some oil (good for the choke threads as well as keeping the slide slick) in a plastic box. It's around $30.