In terms of neural nets, people have more or less done the hard work for you. Typically you'll want to take an empirically well-performing network like VGG, ResNet, Inception, etc and then re-train the top few layers. There is ongoing work in the field to try and train the structure of the network as well.
If you look at Kaggle, the vast majority of winners do so using ensembles. In a recent example - Iceberg or Ship - the winning team used a bit of feature engineering and apparently over 100 ensembled CNNs:
> We started with a CNN pipeline of 100+ diverse models which included architectures such as customized CNNs, VGG, mini-GoogLeNet, several different Densenet variations, and others. Some of these included inc_angle after the fully connected layers and others didn’t.
https://www.kaggle.com/c/statoil-iceberg-classifier-challeng...
It's an ugly kitchen sink approach, but it works.
most practitioners start with the simplest possible learner, then gradually, and thoughtfully, increase model complexity while paying attention to bias/variance. this is far from a "kitchen sink" approach.
It's a nice theory, and it works intuitively with models where you can ramp up complexity easily (like neural nets). It's less obvious if you have a "simple" problem that might be solved with a number of techniques. In that situation I don't see why you would be criticised for trying say any of SVM, random forest, logistic regression, naive bayes and comparing. Pretty much the only way you can categorically say that your method is better than others is by trying those other methods.
The simple approach actually came up in the iceberg challenge. The winning team won because they bothered to plot the data. It turned out that the satellite incidence angle was sufficient to segment a large number of icebergs with basically 100% reliability. So they simply thresholded that angle range and trained a bunch of models to solve the more complicated case when there might be a ship.
[0]: https://www.manning.com/books/deep-learning-with-python