Just some quick notes for now... this beautiful wood is a little bit tricky to work with. The dust is allergenic, so clean up well and wear gloves when handling the wood.
Purpleheart changes color from a brownish grey to a deep purple color, the depth of color is dependent on the wood, with exposure to light. The culprit responsible for the color change is a water soluable dye that is produced in the wood. By wetting the wood after cutting it, you can bring more of this dye to the surface of the wood and this can have the effect of deepening the color, but only after appropriate exposure to light. After sanding to 220 grit or past this, let the wood sit in sunshine for a day before beginning to apply finish.
Various postings elsewhere on the internet claim that the color change is due to exposure to oxygen or UV light, but neither of these are correct (I've tested in a pure oxygen environment, depleted oxygen environment, and oxygen is a non-factor in the color change). Exposure to a simple 100 watt light bulb overnight is sufficient to change the color of purpleheart, so it's pretty clear that UV is not responsible either. However, UV light will break down the colorant, and the wood will turn brown over time. This color change takes much longer than the change to purple, so consider UV blockers in your finish or just keep it out of direct sunlight and the color should stay stable for a long time.
Don't use waterbase finishes to finish Purpleheart. The colorant that turns purple is highly sensitive to pH, and waterbase finishes are bases. These will cause the wood to turn green. Acids will cause the wood to turn pink, and peroxide will turn the wood yellow. Over time, the dye in the wood will naturally leech back to the surface if there is some humidity in the air and the action of sunlight will reverse most of these color changes somewhat, but a heavy base like sodium hydroxide (which turns the wood near to black) will still have a strong color change in place.
From my own experience, the best finishes for this wood are lacquer (simple and straight forward), and tung oil followed by polyurethane or a suitable varnish. This wood is highly chatoyant and both tung oil and lacquer cause spectacular effects. Shellac is problematic with purpleheart as the alcohol can cause some movement of the dye... the wood in my title image was finished with a tung oil and polyurethane varnish that I mixed myself.