Hi Rick -
I have 4 JTV's - two 59's (1 USA and 1 Korean as a backup) and two 69's (1 USA and 1 Korean as a backup). I was an early adopter of the JTV Variax platform (purchased my first JTV-59 in 2011) and have used all 4 of these guitars extensively on the road and in the studio. I have experimented with most of the typically-used string gauges and brands. 9's, 10's, 11's, etc.
Over the years, I have consistently come back to 10's for use in the JTV59 and the JTV69 for one reason - voicing and tracking accuracy on acoustic models. The electric models do fine with 9's or 11's and the difference in tracking or tone isn't noticeably different in my experience. D'Addario does make a 9.5 (hybrid) string set in their NYXL line and I do occasionally use those and they're OK too. If you want something lighter than a 10 you might try those.
My recommendation is to stay with 10's and - if you can stand paying a bit extra, go with the NYXL D'Addario 10's. I haven't found a better playing, better sounding, or more durable string set for my JTV's than the NYXL.
Congrats on your purchase of the 59. I have never regretted my Variax purchases. The 59 is just a beautifully crafted and playing guitar, even without the Line 6 Variax hardware.
Hope this helps!
Bradley