Privacy, anonymity and Bitcoin are quite sensible subjects to say the least. You cannot achieve a high level of privacy unless you become paranoid. You have potential backdoors and flaws everywhere, so what I like to do is I consider
everything I do as a potential danger for my privacy.
Example: you want to transfer funds from your Electrum wallet. The easiest way to do it is just go to the Send tab and use the simple UI to send a tx. However, the convenient way of using Electrum to send txs may harm your privacy because you might end up using together anonymized with non-anonymized coins. The solution is..
coin control.
If you want to break the chain of coins linked to your identity, you could consider:
1. Using Bisq and/or HodlHodl as an exchange for your future transactions
2. Using a reputable mixer such as ChipMixer
3. Using Wasabi's CoinJoin to join coins together anonymously (remember: you need a minimum of ~0.1 BTC to do that, the fees may be higher than you wish and you will get a change
you should take care of.
4. If you're not in a hurry, you could even use
JoinMarket's Yield Generator to
make (very small amounts of) Bitcoin while continuously anonymizing your coins.
Jumping from exchange to exchange only probably makes an authority question your txs even more than they would normally do so. Imagine having 2 suspects out of which one of them exchanges normally and withdraws to their personal wallet while the other just keeps jumping from deposit to deposit addresses.
The cheapest way to anonymize your coins is currently ChipMixer or JoinMarket. Out of these two, the most convenient is ChipMixer.
Remember: if you mix/join coins,
be careful not to ever use them together with non-mixed/non-joined addresses again! 
