Wood – Should I remove vinyl flooring before laying down hardwood

First, remember to lay your wood perpendicular to the floor joists. Laying it parallel can cause a waving effect which is unpleasant.

Next, find the longest, longest, straightest wall which is perpendicular to the joists. Measure out two feet from the wall all the way down the wall. Then find the best line down these marks, snap a chalk line, Measure back to the wall about 23 and 5/8 inches. Snap a this line. Line up your first run of floor against this line, tongue side out (nail through the tongue).

As for room to room, if they are really out of square with each other, try building a transition between rooms:

----||----
----||----
----||----
----||----

This allows you to lay each room separately, allowing each room to be square.

1/2" subfloor is definitely insufficient, so I get why it was reinforced.

3/4" particle board... that is not structural. It's paper dust and glue. A little water and it loses all cohesion.

Simply for peace of mind, if it were me, I'd remove the particle board and put down either OSB or plywood. Probably OSB, only because it's a little stronger (not much) but it's also more expensive so if budget were a concern, I'd go with equal thickness plywood. Either will do you.

But the particle board? Get rid! Its probably not gonna fall apart on you, unless you have a spill... but why even keep that worry?