My wife and I are getting ready to install wood flooring throughout the 1st floor of our house. Our floors tend to be very slightly spongy. While this does not bother me, it drives my wife crazy. I installed steel along the floor joists underneith which has taken most of it out.

My question is, considering this, which type of flooring would help this situation, or better yet, which type would be more succeptable to damage because of the existing condition of the floor, engineered,or solid wood?

Also, what would be better, gluing or nail/staple?

3/4 nail down solid wood. Always.

Any hardwood floor is going to eventually cause different problems if the subfloor is "spongy". I would consider sheeting out the existing subfloor with plywood first, to firm it up.

Right now I have 3/4" OSB down for the sub floor. What would you recommend that I sheet over top of it?

Typically I would go with 1/2" ACX plywood, screwed & glued, offset by 1/2 panel in each direction to the existing subfloor. Ofcoarse I'm not able to walk on your subfloor to see how it feels. I'm not sure what "very slightly spongy" means. Also I dont know your joist spacing. And IMO it's not typical to have to add steel under the joists, or maybe it is with your home, and I'm not aware of this ?
You also have to take into account your height clearances and transitions , adding the additional height of the flooring your considering.
When you get to the point of installing the hardwood , it should run perpendicular to the joists.

Thanks Howard. I think I like the idea of of the ply down screwed and glued. I think the combination of that on top of the sub floor I have, then the 1/2" engineered floor that I select should give me the solid floor that my wife is looking for. My joists are 10" @ 16" on center.

Also, can you get the ACX T&G, or does that really matter when it is installed on top of an existing sub floor?

You dont need t&g plywood when installing over an existing subfloor.

The problem is where to get 1/2" ACX T&G? If I went 3/4", plus the flooring on top of my existing OSB, it would be too much...

Underlayment grade plywood's like ACX fir, BCX pine are square edge on 4-sides. No T&G is called for here because the existing walls would get in your way trying to install it. Subfloor grade plywood/osb are T&G'd.

So even though the ACX is not T&G, when glued and screwed down on an existing sub floor on OSB, it will add a fair amount of rigidity?

Yes.
And the hardwood itself will add further stiffness to the system.

Ok, thanks for the advice.