Most gas efficient way to move ETH to multiple places

I have ETH in Coinbase Pro that I want to do three things with:

- Buy Rocketpool's rETH (effectively staking ETH). I know this can be done through Rocketpool's website. It is more cost effective to purchase rETH through layer two options (I know it can be purchased through Arbitrum), but first you have to pay the gas to get it on layer two.

- Explore layer two technologies to get a feel for what layer twos I might want to invest in (i.e., Loopring, Optimism, Arbitrum, Polygon)

- Move ETH to hardware wallet

I'm wondering if there is a smart way to do this, such as move it all into a layer two in one transaction, and then disperse it from there once you are paying the lower layer two gas fees. Any recommendations for the most gas efficient way to do this would be appreciated!