I really like @Mark_Bailey 's statement about trying things in JMP. One of my pet missions was to always encourage people to NOT try and pick the 'best', whatever 'best' actually means, modeling approach BEFORE any modeling work is done. Try a bunch and see which one works for your particular questions, data and problem at hand. Standard Least Squares, General Linear Modeling, Tree Methods, Penalized Methods (if you have JMP Pro), Neural Networks, and on and on. Try them all, and to paraphrase Mark, "...you can't break anything."
I used to tell my JMP users, it's so easy, your just moving around electrons in the software...go for it. It would be a shame to leave something untried for so little investment in effort.