I don't actually own a lot outdoor gears beyond my snowboarding stuff, so when I was first researching the packing list for Kili it seemed pretty daunting. But eventually I realized that it's honestly not too bad. My tip for you is to not stress, bring what you can from home, and rent the rest when you get there
The towns of Moshi and Arusha (which are the main base towns for most climbers) both have a lot of gear rental shops that cater to climbers; and they've been doing this for many years and you really won't have trouble getting anything you might need. They also provide recommendations of what you're going to need as well, so you really don't need to do too much research
Most tour operators all provide gear rental services as well. Check prices with them before you leave, and do some shopping when you're in Moshi or Arusha
The cost of rental typically range from US$100-$150 per person per trek. Have enough USD cash with you as some of them may not take credit cards
This company came up during my research as one of the more established equipment rental shops (they're based in Moshi)
In terms of what I brought from home to Tanzania, it's mainly clothing and personal hygiene stuff. Here's the list of the main stuff I brought as a reference:
Clothing items. I basically packed as if I was going to the beach and a ski trip at the same time
Hiking boots
Summer t-shirts and shorts
A fleece jacket and a waterproof outer shell
My winter coat
Underwear and socks (regular and thermal)
Winter gloves
Sunglasses
Personal hygiene and medicine
Sunscreen
Lots of wet wipes
Tylenol for headaches
Imodium
Water purification tablets (I just got them off Amazon)
A small backpack to carry my electronics, documents and other little stuff. The bigitems are all carried by the porter (guide and porters come with all the toursand they're mandatory for all climbers)