Great find for you! Don't be in a rush to refinish them though--try a good cleaning first, and waxing. So many people like that plasticky gym floor look that poly gives, so right away decide to sand--I don't think it looks right in an old house.
I know you will have a wonderful time prying up all the staples from the padding--I still find some in my bedrooms--and the downstairs hall was done with tacks--lots and lots of tacks since no single piece of padding was larger than 2'x2'. :)

Be happy if it's tacks and not glue! Some mentally deranged person put glue down in the music room to keep the area rug they had from moving. You've never seen such a nasty mess!

That *is* exciting!! And I second what columusguy said ~ I just did a trial waxing on a few of my floors and I love it. Save the patina, put on a layer of protection and refresh them all in one shot. Of coarse if you do like the "gym floor look", it's your floor to do with as you please ;) I posted a few before and after pics of the floors I waxed, for reference. Just search a few posts down....

Nope, no high gloss plastic finish for me!!!! All it needs is a good washing to get off the flecks of padding that are stuck on and a coat of wax. If I wanted a brand new looking floor...I'd have just gone to the store! I want character, and patina and age! And I got lucky with the staples...they only used them where the seams were :) so there aren't many!

The sitting room was never painted (yay!!) The bedroom apparently had a floor cloth and they painted around it, with a yellowish milk paint. The milk paint is worn in the traffic areas...and the square in the center that was protected is just beautiful aged wood. I'm not going to sand off that milk paint. To me, it tells a story :)

We had indoor/outdoor carpet glued to our hardwood floors. Murphy's Oil Soap was what we used to get the foam that was stuck after we removed the carpet.

Thank you Mary! That was what I was about to ask!!! Today I am cleaning the floors and I had no idea what to use! Our foamy stuff isn't glued down...it comes off easily...but it is stuck to the floor due to years of people walking on disintegrating gummy, old padding.

I'm so happy for you right now I got that happy butterfly feeling in my belly! And I totally get that "unwrapped gift" thing. There's a hole in my dining room silver/linen closet thingy to prove it!! I had to see the lath and what's behind it for whatever deranged reason my mind came up with! Congrats on a great discovery!

"try a good cleaning first, and waxing."

Cleaning yes, waxing no.

Using wax can interfere with future refinishing by contaminating the surface so that a new water based finish (and even some solvent based) will not adhere proposal.

Even if you sand the floor, wax can still be in the cracks between the strips and cause problems.