If you look online, you can find tools that don't necessarily show you the best block for a certain HEX code but it will auto-generate your image or drawing into a whole mural of Minecraft blocks for you.
The first one has three unique versions for different version of the game which provides you with a bunch of options for block types and options to remove certain blocks that you don't like/have. Its made by PyroStunts: HERE
The second one that I found seems to let you manually edit and place pixels as blocks so you can see different combinations yourself while also auto-generating the pixel art for yourself. This one was made by Explodey54: HERE
This might not be the best for you but it will provide the best colors since the generator will provide blocks that look the most like the original image.