The amount you are trying to send does not influence the price of transaction, just how complex the transaction is (larger transactions require more bytes in the memory). If you want to send 1 BTC and have an UTXO pay with it will cost you less than having to construct a transaction with multiple UTXOs whose sum is equal or greater than 1 BTC.
The fee is nowadays automatically determined by your walled based on how many transactions there are in the mempool. If there are a lot of transactions pending, you will have to pay a larger fee to get your transaction confirmed faster since miners will usually pick the transactions that pay more per sat/byte.
You can set this fee yourself as well