Is there a minimum Neuron balance?

The minimum balance for the Neuron wallet is 0 (as in nothing is "on-chain", likely because the wallet is brand new) or 61 CKB (the minimum required to be considered “on-chain”). You cannot have something in the middle, like 30. Additionally, it is recommended that you have enough CKBytes free to pay for transaction fees. The Nervos community suggests reserving around ~200 CKB (~5 USD) for fees.