Any non-custodial wallet won't ask for KYC. Those who ask for KYC are mostly exchanges. Start by reading the OP until you understand everything mentioned, and decide whether you want to run a node or node. If not, and you plan on using a PC, Electrum is usually a good wallet to start. On mobile you have Samourai. But as always, do your own research first, don't follow any suggestion blindly. Make sure to verify any files you downloaded from the internet to avoid malware.