Is a basic neural network architecture better with small datasets? I'm currently trying to predict 1 output value with 52 input values. The problem is that I only have around 100 rows of data that I can use. 

Will I get more accurate results when I use a small architecture than when I use multiple layers with a higher amount of neurons? 

Right now, I use 1 hidden layer with 1 neuron, because of the fact that I need to solve (in my opinion) a basic regression problem.
I'm not aware of a direct way for finding the best NN architecture for a given task, but the recommended way, as far as I know, is to devise a network that can overfit the training data, and then apply regularization on top of it.
That way, you can be almost sure you're not underfitting/underperforming due to network capacity.