Hello! You are really going to fall in love with this cute little Axolotyl!
My daughter Temple has one and LOVES it! Here is a pic of her "Boo" She has it in a 20 gallon long tank, but he will need something larger soon. By the way, she removed the sand she had in the tank and replaced it with ceramic tiles because Boo was eating too much sand and actually throwing it up. Had stopped eating... now after the tiles were laid down he is eating like a little pig!!
They have a fantastic ability to regenerate and grow new appendages, etc. so your guy should heal pretty quick as long as his water quality is good.
You are going to have to cycle that tank tho so watch your water parameters carefully every day until it cycles. What Temple did is she got an Internal tank filter like the one in the pic below. She dropped the water level so the filter just trickles the top of the water. She uses Prime water conditioner and API Quick Start to get the cycle started, but this product will not cycle the tank it will just help keep the Axo alive while the beneficial bacteria is building up in the filter. You will still need to monitor water parameters very closely as this is happening (recommend API Master Test Kit) and as ammonia and nitrites appear do a water change and add in more API Quick Start and Prime. Once you start seeing less or zero ammonia and nitrites, the nitrates will start kicking in (this should mean your tank is close to being cycled) Watch your water parameters closely for at least the first month or two until it appears the tank is cycled and then at least 1x a week thereafter.
The In-Tank Power Filter
Tetra Whisper In-Tank Power Aquarium Filters - Filters - Fish - PetSmart
Looking forward to seeing your pics!