Which neural network topology is the most efficient to generate randomly shaped letters?
I think it's unlikely you're going to get good results.  Neural networks typically require a large training set.  With only a few dozen or so examples, I doubt you'll have a large enough training set for this to work well.

So, what could possibly go wrong?  I suspect the most likely outcome is that you'll get useless results.

That said, if you really insist on trying neural networks, you could try using a variational autoencoder.  An autoencoder consists of two halves: the first half maps the input $x$ to a value $z$ in the "latent space", and the second half maps $z$ to an output $x'$.  You train the autoencoder to ensure that (hopefully) $x$ and $x'$ are very similar, for all the instances $x$ in your training set.  The idea is that you make the latent space much smaller than the space of inputs/outputs, and you hope this forces it to generalize.

For instance, the input might be a 40-vector $x \in \mathbb{R}^{40}$, encoded by a one-hot encoding ($x_i=1$ means that you include a black line in the $i$th position; $x_i=-1$ means you don't include it).  The latent space might be $\mathbb{R}^2$ or $\mathbb{R}^3$ or so.  You might include a few layers of a convolutional network to map from $x$ to $z$, and then the inverse architecture to map from $z$ to $x'$.  Then, you could train the network using a standard loss function for variational autoencoders, along with some regularization term.