When to go to Moscow

I went last June, and the weather was perfect. Russia does get fairly hot and humid in summer, so that could be a plus or a minus, depending on what weather conditions you prefer. Winter is cold, snowy, and windy.
Overall, I would recommend spring or summer for Eastern Europe and Central Asia. Foliage and colorful flowers go a long way in camouflaging what may look grey and dismal in winter.
As to what to pack, my number one pick would be cash. Cold, hard currency. ATMs are suspect at best, and travellers checks are very difficult to use, especially if you're looking to travel outside of the city, which I would highly recommend. Bring as much cash as is allowed by customs, and hide it all over your body in various pockets, money belts, etc. Being able to only pull out what you want to change, as opposed to a large roll of money, can be very important.
Whenever you go, and whatever you bring, you are going to have an amazing time. Moscow is a breathtaking city.

The best time to go depends on your definition and cold tolerance. We went in the summer (July), which is the normal tourist season because that's when the weather was most comfortable. But you also have to share the city with more tourists from everywhere. If you go in the winter, it's cold, and maybe there is snow on the ground, the days would be really short, but that may show off what Moscow is really like, and the attractions would be all yours.

What to pack? definitely your camera and memory cards/film. Umbrella, sunglasses, hat, money belt to put your valuables in. If you do go in the winter, more warm layered clothing, otherwise, it's not that different from what you would pack going anywhere else.