If a unit with the trigger condition "when this unit attacks" attacks a zone with a support with the trigger condition "when this zone is attacked", which action will trigger first? I know that zone to be attacked is declared first and then attackers, but not sure about this. Thanks.

Both triggers are met at the same time, since a zone is only considered to be attacked when attackers are actually declared (declaring the zone but then not declaring any attackers isn't enough). So then you follow the steps after a trigger condition has been met, as described in the FAQ.

1. Active player resolves his triggered constant effects in order of his choice.

2. Next player resolves his triggered constant effects in order of his choice.

3. Active player resolves his triggered forced effects in order of his choice.

4. Next player resolves his triggered forced effects in order of his choice.

5. Starting with the active player, players take turns putting triggered actions on the chain, until all players pass. Then the chain resolves in reverse order (last in, first out).