No, there is no one crop that works better than another. That rumor started because within the first couple of days of T & T starting ONE person got it by harvesting a few strawberries. Numerous posters here then went and planted and harvested hundreds of strawberries, constantly maxing out and starting over and no badge. Its just a numbers game. You just have to harvest hundreds upon hundreds of crops until you hit the magic number. I cant remember how many, theres several posts somewhere on here, that gives the number that seemed to work for many people. My recollection was maybe 500? But dont quote me as its been 6 months since i finished T & T and the numbers are all a blur.
Regarding that first player to get farmer's with a few strawberries in the first few days. My opinion is that it was a glitch. There's always a small glitch when new goals are released and i think that this was one of them, where some players' systems registered their progress from the start of their game and not from the start of the goal. Just my opinion but after that, i don't believe anyone else got it so easily. Just keep plugging along, it'll happen at the moment you decide to give up!