Honestly, I would say Pirate Invasion, simply because the furniture you get from it sells nicely, the accessories and weapons are extremely useful (eg. Greedy Ring and Coin Gun) and the two bosses each add something interesting that isnt added by the other two invasions, since the Martian Madness' boss is the Martian Saucer which is essentially, if you dont have a box, get ruined. While the goblin army only has a boss in hardmode, and while she is cool and all, she doesnt have much long term use.
But the pirates, they have the Flying Dutchman, which volleys you with cannon fire and pirates, but also drops a trophy and assorted goodies, and the pirate captain, which will ruin you if you dont notice him slowly and dramatically walking about.