Replacing livingroom floor 24x22. slopes in places and raises in others. cannot use carpet because of pets and

Question:vinyl is out of the question. laminate is free floating and im concerned that it will leave bubbles in the floor at the uneven arears. what would you suggest as far as leveling the floor and what type of flooring would work most efficently ? the existing floor is crappy vinyl squares on a partical board subfloor that must come up. my contractor is scratching his head and possibily my wallet if he makes the wrong decision. please help

Answers:
When you take up the sub-floor, you'll probably find some of the joists are sagging. There are two solutions to this.
1- jack up the floor and replace the bad joists.
2- "Sister" straight boards to the existing ones.keeping the crowns up. and leveling as you go.
When you get all that to your liking, ...lay new sub-floor, but for God's sake DON'T use particle board, 1/8th'" plywood is fine. Also, use screws, don't nail it.
A nice hardwood floor will last a long time, and there seems to be a lot on sale at Home Depot these days. If you prefer tile, You'll probably need to level the floor with, well, floor leveler. get as much as you need (read the bag at the store) and work quickly, the stuff dries very fast. Use a decent tile and your floor will be fine for a long time