I think the first thing that I would do would be to evaluate the data that you have already. The Evaluate Design platform will help (DOE > Design Diagnostics). It can tell you about the power and the degree of correlation between effects.
You might find that the data you have is useful in determining the important factors. And you could augment this with additional runs to improve the information.
If you were starting with no data (or if you decide that there is no value in the data that you have) then a definitive screening design would be a good approach because it is efficient in screening a large number of factors: 33 runs if all factors are continuous and you select no additional runs. A compromise is that you can't estimate all 2-factor interactions but you generally expect only a handful to be active. Again, you can then augment to improve information about the active factors.
You might find my blog series useful if you are new to concepts like correlation between effects.