Use Tor for the privacy as that's going to be easy and helpful at the same time. It would be difficult for you to run your own personal node but that's also a good option.
You must run your own node for better privacy, just using Tor alone is not enough if you are going to connect to a third party server that can see your BTC addresses.
Electrum is a SPV wallet and you have to connect to Electrum server to broadcast your transaction. You can increase your privacy a little bit by using Tor with Electrum wallet but it is not a best solution.
You must not connect to a third party server when using electrum, and you must not use a full node wallet for better privacy, you can use your Electrum wallet and connect to your own Electrum server, without exposing your ip addresses and BTC addresses to any third party server.