Removing tile flooring is a messy job. Expect flying chip fragments, mortar dust, and plenty of debris. Protect the space with plastic sheeting and drop cloths, and gear up with goggles and a respirator before you start prying. Pros keep the mess in check by attaching industrial vacuums to their tools, a setup that captures dust at the source and leaves the work zone far cleaner than a DIY approach.
Removing the old tile first is almost always the smarter play. If you tile over worn or uneven flooring, the new surface can crack, pop, or sit higher than the surrounding rooms. Fixing that later costs far more, especially if you need to re-level the floor. By demoing the tile now, you get a flat, solid subfloor and avoid surprise repairs down the road.