"What types of screws do you use for this?"

Anything excet drywal screws.

Try McFeeley's.

You can even rent a drill that allows you to stand up and drive paper collated screws.

Yes, screws should correct your squeaks. And wood screw wood be fine.

I guess my question is: Why are we replacing 65 year old wood flooring with the stuff that is sold today? I am concerned that you might have been ill advised...

Thanks. Main reason is the noise from the existing floors. When you walk around on the floors it sounds like bombs going off (a bit dramatic). It's the subfloor planks that have come loose from the joists. The nails are moving and it is so loud that my two kids wake up at night if I walk over their rooms. It is affecting the enjoyment of the house and I can't fix it without tearing out the existing floors.

Wouldn't it be cheaper to re-use the old flooring? You may lose a few boards at the edges, but nearly all of it should come up fine.

They make special screws for exactly your problem. They're designed so that the screw head breaks off just under the surface of the wood leaving just a small hole to be filled.

Tom Silva of Ask This Old House demonstrates how to use the product in the attached link. It's the last segment of the show.

Here is a link that might be useful: Ask This Old House

I would seriously try to salvage - or at least sell to someone - all that maple strip hardwood.

Relay as much as possible in the main public areas, then fill in the less visible areas with modern flooring.

No wood you can grow now will be as good as that old wood.

If the underside of the floor is accessible from below, you may be able to drive screws from there

Thanks for the tips. I've pulled up a few strips to test how it will go and it is so dry a lot of it just splinters and cracks. The planks underneath look like they were salvaged themselves...some are one by ten, some one by six.
Also looking for any suggestions on how to remove the hardwood strips that are underneath some cabinetry. I had some custom cabinets installed over top of the existing hardwood floor some time ago. They can't be moved. Someone suggested using a dremel to cut the hardwood flush to the cabinet. Not sure there are any other techniques.

I forgot about the screws mike kaiser mentioned! I'd use those where needed, and fill the holes...and keep the original flooring you have. Fill in the few you took up with newer or salvaged wood.

It's splintering and cracking because it's maple - hard, durable and brittle. And prying boards up is guaranteed to destroy them. You have to remove them by reversing the motion it took to install them.

The screws look like the easy way out, and the least expensive, if you haven't reached the point of no return on the removal.

If you want to salvage the wood - and it's selling for $5+ per square foot as salvage - buy an oscillating multi-tool and several metal-cutting blades. Slice through the nails under the boards and coax the board loose. If you can work from the side with the tongues, the nails are accessible and the boards easiest to remove.

It's faster, and easier and saves more boards.

Remove the molding and use a wood-cutting blade on the multi-tool to slice out around the cabinets, but accept that it's going to be difficult to impossible to do a clean job, and the new floor will abruptly end at the cabinets. If appearance matters a lot, remove the cabinets, take up all the floor, put down the new floor and re-install the cabinets.

Appreciate the advice everyone.