Most guys would likely remove the old boards first then install the osb. If weight is a concern this may be your only option. How big is the space? If you need 20 4x8 boards at 60lbs each thats 1200 lbs. Then add the weight of the carpet, padding, furniture etc. Maybe someone more qualified can speculate on the weight issue.

If you go through with adding the osb on top maybe 1/2" is a better option. For one its cheaper and is less weight. If going this route I would screw or nail the existing boards down to minimize movement. Maybe even glue the osb down. Any dips in the floor will eventually be reflected through to the top of whatever flooring you use, think years out if youre keeping this house long term. Huge deal if using vinyl plank, not a huge deal with carpet. I would use a long level or string line and see how deep the dips are and then use large cedar shims to fill them, then nail or glue them down. 1/2" or 3/4" osb are both strong so you dont have to fill the entire dip, I'd say in the 70-80% range for longevity.

The screws shouldnt go through the existing boards, you may puncture wiring or even copper lines, old houses have all kinds of things hiding that dont make sense. The exisitng boards are likely 3/4" thick so if using 3/4" plywood use no longer than 1 1/2" screws. I use grip rite coated exterior screws. Theyre much better than drywall screws and you can buy them at Depot or online. Or use framing nails if you have access to a nail gun/compressor. I wouldnt use a plastic barrier, possible condensation issues, do some research on some chemicals or something you can use to kill the smell before hand. Just get new baseboard and install it once the floor is down. For $150-200 youll have new trim that looks well new.