Looking for advice on best double j saddle. I ride 16inch Martha josey now. Looking for something that's is secure. 

Double J has so many your best bet is to find a dealer that has a place you can ride several.

Most people think that a high back and deep pocket is more secure, but some folks (me) find them painful to ride in.  And seat size is important, too small a seat and you’ll be more likely to pop out and be insecure, in my experience.

plus double J offers so many different trees you’ll want to find the best fit for your horse as well.

What OhMax said. Or, if you can find out when/if their saddle fitter will be near you, take your horse to be fitted and find out which tree(s) are your best fit for the horse and go from there. 

I ride in a LM Nueva, bought new in Feb. Love it! I did have the horse fitted prior to buying.