Some assumptions must be identified when looking at different types of metals.

1) Historically, jewelry manufacturer have, for decades, plated 14k white gold with rhodium to produce a much whiter appearance. When a wearer remarks that her ring is turning yellow, in reality what is happening is the plating is wearing through and she is seeing raw un-plated 14k white gold under the rhodium. The simple fix is to re-plate, typically less than $125 to reapply for most rings. Cheaper sources will re-plate for as little as $30, but beware the coating is low grade metal applied too thin to last.
white_metal_12) Palladium was last used as a viable jewelry metal during World War II since platinum was a strategic metal and was used for the war effort. From the late 40’s to after 2000, platinum was not priced significantly higher than gold and palladium was hence unimportant. Now that platinum has tripled in price across the as few years and the price of palladium has remained consistent, palladium is again an important jewelry metal.
So, how to decide?

14k white gold has a natural light yellow cast to it. Some find that attractive, most prefer to plate it with Rhodium and maintain it as a whiter look.

18k white gold is notably whiter and rarely requires plating to remain white. Its whiteness is very near the color of platinum and the surface is hard, allowing it to retain a polished surface better than either of the platinum group metals.

Platinum is undoubtedly the whitest metal, with great lasting properties but very low surface hardness. Platinum wearers will always remark on the loss of polish as it is worn, to the point of appearing satin finished if not polished frequently.

Palladium is just as white as platinum. It has a slightly harder surface so it holds a polish somewhat better than platinum, but not as good as 18k gold. Its advantage is that it weighs less than either 18k and platinum and usually is priced slightly higher than 18k but well below platinum.

Neither palladium nor platinum require any plating to maintain color.

Our recommendation:

Come look at the metals. Feel their weights and look at the colors. The manufacturing process allows the metal decision to come at the approval of the wax model, so you can wait until the exact differences in price can be laid out for you, specific to your ring.