Question about transfers from cold wallet to exchange

Hello everyone! Still new to the crypto world (started to learn about it 3 weeks ago) and I am glad I learned so much in that time frame.

I did transfer my ETH from the exchange to my cold wallet (Ledger Nano S) but I have a quick question regarding fee's for transferring back to the exchange.

The thing is the exchange I use covers fee's for transferring to another wallet, so I have no idea about what the cost/fee would look like.

My question is, for transferring crypto (ethereum in this case) from my cold wallet to another wallet (exchange in this case), do I get to select at what speed it would get transferred and do I see what the fee would be? Or do I just have to look on a website and do the math myself for how much the gas price is?

I'm preparing for when I want to stake my eth 🙂 .

Thank you for helping me out and good luck on your trades/investments!