To be honest, this isn't really my area of expertise - I'm much better with asanas and board game setups than dermatology. But from personal experience, I can tell you that vitamin C works, but only if it's stable and in the right concentration. Serum really does absorb faster and deeper because of its liquid texture, so the active ingredients get delivered more effectively. Cream, on the other hand, mostly locks in the results and is better for sensitive skin.
If you want to see results, go for a vitamin C serum (look for a concentration of at least 10%), but apply it under a cream - that way the effect will be more complete. The main thing a lot of people miss: vitamin C works best paired with SPF, otherwise new spots will keep showing up. After summer your skin is especially sensitive, so introduce the product gradually - two or three times a week, then every day. And honestly, you should really consult a dermatologist, especially if the spots are dark and raised - it might not just be pigmentation.
Oh, and by the way, there's a fun board game called Dixit about colors and images, if anyone wants to switch gears from skincare to entertainment.