Greetings and welcome to the forum.
I am no tire/tyre expert so this is anecdotal based upon my personal experience.
Several years ago I bought a somewhat neglected 94 K1100LT, it had 52,000 miles on the odometer. There were bias-ply tires on the wheels, I do not recall the manufacturer and model type. Over the course of several months I rode it for a couple thousand miles before I parked it and performed a thorough inspection and maintenance cycle during which I replaced the old bias-ply tires with radials. I chose to do this based on conversations and information found on this forum and I had never rode a motorcycle with radial tires.
My choice of tires were Michelin Pilot Road series, PR3 for the front and PR4 on the rear.
The difference, for me, was immediately noticeable and remarkable. Smooth riding, tracked straight and true, confidence inspiring and longer lasting. The bike now has 86,000 miles and I have used the same type tire since.
Again, my experience for every forum member you will have another opinion/experience. You may also have to select another tire size to find ones that fit your wheels, lots of info on that here on the forum.
Also, it is a commonly accepted good practice not to mix radials with other type tires.
By the way, One of the best riding manuals I have ever read hails from your neck of the woods, should be required reading for all riders!
http://nmcu.org/files/Full%20Control_2013.pdf