As an optional building at first, you may choose not to purchase the post when it first becomes available to you, I cannot pass judgement, but I will say this, buy it early while you can, it only hinders your progress later in the game when it becomes part of a quest (for more information, see here). The only downside to buying it earlier on comes from the fact that, as you progress through the updates in the game, buildings drop in price. Whichever you do, you do need to build the post office eventually.
The Post office does not come with a new character, and, like many other buildings in the game, has very limited character interaction. The only two perks of getting this building is the income of $120 and 12XP every 6 hours through the task “Putting up ‘Wanted’ Posters”, and the fact that, it being a public building, it adds to your Obedience level in the 5-star rating system.