Q. I was thinking of using the Electrum wallet. Are there any better options?
Electrum is surely a good option.
Q. Any concerns with installing the watch only wallet on my regular daily-use PC instead of the dedicated crypto PC?
The watch-only wallet doesn't contain any private key and there wouldn't be any problem unless there's someone else using that device and you don't want him/her to know you own bitcoin.
Q. Are there any best practices for setting up a watch only wallet?
Unless you care about your privacy very much, you can easily import your master public key into electrum and create a watch-only wallet to see your transactions and your balance.
With creating a watch-only wallet on electrum and connecting to a server, the server owner will know your IP address and can link it to your addresses.
Q. The biggest risk seems to be accidentally sending the private key instead of the public key. Is that foolproof on modern hardware wallets (e.g., do you have to go through a stupid amount of work to get the private key, making it less likely to screw up) or is there something to watch out for?
Why should you to send your private key to someone instead of your address?
You don't need to save the individual private keys at all. All you need for recovering your wallet is your seed phrase.
Q. Do public wallet addresses always start with 1 or 3 (which something I'd read)? How many characters long are public keys compared to private ones? Is there some other high confidence way confirm the string is the public key and not the private one?
Bitcoin addresses start with 1, 3 or bc1.
The most common format that is used for private keys is WIF. Such private keys start with 5, K or L.
Q. What blockchain explorer would you all recommend using?
I usually use blockchair.
Take note that the block explorer can watch your activity and with using a block explorer you may hurt your privacy.
Q. Do I need to set-up a full node to do this (i.e., is it really necessary)? If so, should I set up the node on my dedicated computer, or on my regular daily use PC? Does it matter?
If you want to protect your privacy completely, then I recommend you to run a full node and use bitcoin core or run your own server on electrum. Take note that for running a full node, you will have to download around 450 gigabytes of data.
Q. Lastly, can anyone help me understand the concept of sweeping and if it's something I need to explicitly do? Does ledger automatically take care of that?
With sweeping your private key, you send the fund from the address associated with that private key to your wallet.