I mostly hand make my animal themed gifts from polymer clay. I use Fimo but you can buy other types. Polymer clay is an oven bake clay that lends itself to making jewellery and gifts because its hardwearing, long lasting and waterproof.
Its pretty easy to start using and moulding something. Just let your creativity flow! I have started to make larger sculptures that incorporate not just polymer clay but air dry clay. I’ve added some pictures of some bigger pieces I’ve made like ‘Loopy’ the fancy octopus! You can also mould polymer clay around a structure using wire or foil to help with larger projects.
You can find some tutorials to make some items and gain some tips on my youtube channel.