After the swap, when you receive your first transaction on the Monero wallet (I like feather wallet, it’s like electrum), moving funds to another sub address or a new wallet is good. Running your own node is very nice but if you don’t want or you can’t, you should use Tor (preconfigured on feather wallet to connect after block sync, nothing to do especially). The goal is to hide your IP to a remote node and be even more anonymous