Wiring – Ceiling light with push connector but 3 white wires in box

If the old fixture worked, at least one of the white wires is hot.

The easiest way to check which is hot is to use a non-contact tester. If the fixture is already removed, leave the two wires bundled together with a wire nut over the end. Put a wire nut on the single white wire. Turn the breaker back on. Only one of those should register on tester. That is the hot side. The other should not register. That is the neutral.

Once you know which wire is hot, mark it with black tape or a permanent marker.

If the the fixture is still attached, you can do the same thing with the fixture hanging down. Once you know what is what, turn the breaker back off before wiring.

The black wire goes to the hot wire, the white to the neutral. The ground wire should be attached to a green or bare wire if there is one in the box, or to the box itself if it is metal. If not, just cap it.

Both black and red are typically used to indicate hot. Though you can't be positive without actually testing it with a multimeter. Red is usually used when there are two hots (14/3 wire instead of 14/2).

Both green and bare copper are used to indicate ground.

So it sounds like you wired it correctly. The green wire from the line (source) should also be attached to the green grounding screw in the electrical box.