I wonder which "wallet-ui-label-network" should I choose. I see there are BSC, BTC, BNB & ETH networks.
You should read their warning that means both from and to address should match with each other on a same network.
Please ensure your receiving platform supports the token and network you are withdrawing. If you are unsure, kindly check with the receiving platform first.
BSC's miner fee is lower than BTC.
Not correct. It is not miner fee but a withdrawal fee charged by Binance.
In addition, BSC is not a Proof of Work blockchain so no miner on that chain. Usually withdrawal fees from exchanges are more expensive than average transaction fees on blockchains if you make your transactions from non-custodial wallets.
My BTC address is generated by Bitcoin-core official client. I don't know what kind of network does it support. Can I choose BSC and send my BTC to my address? Or it wouldn't work? Must I choose BTC network?
Because of your receiving address is Bitcoin address (real Bitcoin, not a token on BSC or other chains), you should choose BTC (Bitcoin) on Binance to submit your withdrawal request.
For your receiving address, from Bitcoin Core, you should choose Segwit type because with this address type, later you will have to spend less transaction fee.