If you want to eliminate any possibility of succumbing to Fools Mate, play 1.e4. This is the King's Pawn Game and the first advantage of it is you have sidestepped the two move defeat. Multiple attacking options open up for you, not some ignominious defeat that you don't want anyone to know befell you. Let's look at some KPG alternatives.
If you're a gambler, look no further than the King's Gambit. Kiss your f-pawn goodbye, and with the open f-file and some quick development, you could be all over the opposing King as the opening gives way to the middlegame. Make sure you know something about the Classical Defense and the Falkbeer Counter Gambit. Sometimes Black doesn't bite.
Other options include the Spanish Game, the Italian Game, the Scotch Game, the Vienna Game, the Bishop's Opening and a multitude of others. 1.e4 puts you on the front foot as you take the fight to Black. As someone who was fairly good at the game once said, 1.e4 is best by test. That was his opinion at least.