I assume that the luan/vinyl flooring that exists in my home should be removed before I install 3/4 inch solid hardwood.
Question is, what would be the best tool for this job?
There is the original vinyl + 1/4" luan + vinyl.

It's always best to remove old floor coverings dawn to the sub-floor before adding hardwood. I set a skil saw to the right depth and score through the layers in a crossing pattern so all the layers will be able to be pried out at once. Remove the fasteners, also. Then you can check to see if you will need to get the floor flat. Sanding high spots is a lot more difficult with old nails or staples imbedded into the sub-floor. Presume there is asbestos in the old vinyl flooring and wear the best dust masts and keep dust from other parts of the house.