Hi,
my old subfloor in the second floor bedroom consists of 5" planks. I was advised to glue and screw 1/2" plywood on top of it. I'm undecided about the actual floor on top of it, but currently leaning toward prefinished, T&G engineered hardwood.

Most discussions about glue deal with installations over concrete. What would be the right choice of glue both under and above the plywood and why?

You should be able to lay a new floor over the existing floor. Each plank probably has two nails each time it crosses a floor joist, I like to add another nail in the middle just for insurance that it will never become loose. You can use a floor stapler with 2 inch staples to fasten it down if you remove the floor plate with an allen wrench. Check to see if there are any bumps or dips with a straight-edge. Any variation more than 1/4 inch in six feet should be addressed. Sand down high spots after you set nails with a quarter-inch punch and hammer. Build up low areas with three-tab-roofing, which is close to 1/8 inch thick after marking carefully with chalk where it is low. Step it up to get it within 1/8 inch before you lay the new flooring.
BTW: If you are going to lay new flooring over the whole upstairs, you will be making your top step out of code. Code is for safety. All the risers should be the same rise. You may need to lay the same flooring on all the steps to keep it safe.
A sub-floor adhesive would be better to glue anything to a sub-floor, latex is best.