How to buy axie on mobile?

Could you please elaborate on the process of purchasing Axie Infinity tokens on a mobile device? I'm particularly interested in understanding the steps involved, such as choosing a suitable cryptocurrency exchange, setting up an account, funding it, and then navigating to the correct marketplace to complete the purchase. Additionally, I'd like to know if there are any specific considerations or precautions I should take while performing this transaction on a mobile device, such as security measures or transaction fees. Could you provide a detailed description of the entire process, including any potential challenges or pitfalls I might encounter?