I have the majority of my crypto on Coinbase with a couple on Crypto.com - is it pretty straight forward to get these off of these exchanges and onto the Nano S Plus?
Yes.
Once you have your device, simply follow the set up guide I linked you to before:
https://support.ledger.com/hc/en-us/articles/4416927988625-Set-up-your-Ledger-Nano-S-Plus. This will involve booting the device up, setting a PIN code, writing down your seed phrase back up, and then connecting it with Ledger Live to update to the latest firmware and install the software for the coins you are interested in.
Once you've done all that, then you can open the relevant coin - bitcoin, for example - and generate a receiving address.* Head over to Coinbase, look for the option to withdraw or send bitcoin to an address, and copy in your receiving address from your Ledger (double check everything, especially that you have copy/pasted the address accurately!) This will send your bitcoin from the exchange across to your hardware wallet.
The very first time you do this, lots of people like to send a small "test" transaction of a few bucks worth of bitcoin to make sure they have done everything properly before sending across their full balance.
*At this point, some people like to reset their device to factory settings, and then recover from their seed phrase back up they've just created, and ensure they generate the exact same address. This allows you to be doubly sure that you correctly copied the seed phrase without making any mistakes.