If you don't have all the necessary equipment then consider renting it from Exodus rather than buying something you may only use once; the quality is very good and you don't have to worry about it not arriving at the same time as you! Make sure you do have proper equipment as the guides will check this and won't allow you up if you don't.
Take a wide-necked water bottle with a good seal for summit day as it is likely that any platypus system will freeze a few hours into the ascent. You will need to be able to carry at least 3 litres of water per day.
Batteries are really expensive in Tanzania so take enough and if you want to leave a gift for the guides then AAA batteries for head torches are appreciated. Our group also left behind a small amount of walking equipment, spare Diamox and water purification tablets and some first aid items.
You can get away with US Dollars only, although you will sometimes be given change in Shilling even if you've paid with Dollars. Most of us exchanged $50 - 100 to Shilling and this was plenty.
Be aware that in many places the credit card machines (including some of the hotels) don't work so take plenty of cash.
There are plenty of opportunities to do laundry so you don't need to overpack.
Don't forget that the luggage limit for the internal flight from Kilimanjaro to Zanzibar is 20kg i.e. less than for the international flights.
Although you do need to be reasonably fit to get to the summit, a certain amount of determination is also needed, summit day is very tough but it is worth it. The other days are relatively easy.