Ok. Here goes my nerdy post. I have a small set of go-to DOEs which I really like to use.
For screening at 2 levels, I like to use the Taguchi L12. I can screen 11 factors in 12 runs. If I don’t use one of the factors, I like to look at the effect anyway, since it is slightly confounded with the 2-way interactions of the other factors, which gives me a heads-up about possible interactions to look out for.
For screening at 3 levels, I like the Taguchi L18. It also captures one 2-level factor and one interaction. Good stuff!
For 2-level modeling, I like full factorial designs. In my experience interactions are much more ubiquitous than most people think. To me, fractional factorials are nothing but trouble for most people. The one exception is the 2 5-1 half fractional factorial. It is relatively safe in most cases.
For 3-level modeling I really like the Central Composite Design (CCD). I like how I can use axial values as needed. But I especially like how I can run the 2-level factorial portion first, along with center points, and only run the axials if the 2-level model does not sufficiently confirm. Good stuff!
If you can get comfortable using these four, you’ll probably be able to handle the most (if not all) of the experiments you are faced with.