KIWI Tokens can be mined with very moderate gear - even a regular laptop finds solutions from time to time. The best option is a CUDA-enabled Nvidia GPU PC that is also a requirement for Cosmic Miner. Otherwise, your option is SS3 Miner, a command-line based miner for all platforms.
For KIWI mining only solo mining is possible - there are no mining pools for KIWI. In solo mining, a miner interacts directly with the smart contract. There are no pool fees, and all concurrent solo miners compete against each other. If two or more miners find a complete solution for the same block, the one with the highest gas price gets the tokens. For others, mint transaction fails and a small amount of ETH gets burned (not much).
Before you start, create or choose an Ethereum address to be used in mining. Send in some ETH for minting tokens. That address interacts directly with KIWI smart contract and receives yout newly mined and minted tokens. As littele as 0.01 ETH gets you started.