Is there anything else I need to store together with the private key (like the hashed transaction number in transaction_input in the blockchain? ScriptSig?)
No, all you have to store and keep safe is your private key. All other information related to transactions like their hashes, inputs... will be saved on the blockchain (publuc ledger) so you don't have to worry about them.
However, you should consider saving the public address related to that private key as well. You don't want to have to derive it each time you request a payment or check your balance!