On my crypto journey I have signed up to various crypto exchanges and learnt a few things along the way (and I am sure there are many things I can still learn). Points include:
(1) The larger exchanges are obviously the safest even though no exchange or online company/entity can ever be totally safe from hackers. These would include Coinbase and Binance (the latter of which has actually been hacked but covered customers losses).
(2) Binance does list some coins on a community vote for free but I am not sure how transparent this is as I own a coin called Electroneum and it won a community vote hands down as it has a huge community of its own but it wasn't listed as Binance seemed to think the votes were not legitimate (but I am not sure this was actually proved).
(3) Some coins pay the big fees to Binance to get listed to get a short term boost to their price but long term this isn't sustained. In addition exchanges may have vested interests in coins so be careful with such coins e.g. coins listed on an exchange offering by Binance.
(4) Quite legitimate coins often list on smaller exchanges which subsequently get hacked e.g. Electroneum was first listed on Cryptopia and subsequently got listed on loads of other exchanges such as Huobi, Liquid, Kucoin etc but since Cryptopia was the first exchange Electroneum was listed on and this site was hacked a lot of people have potentially lost money if they did not withdraw their coins to elsewhere. All coins on Cryptopia are in this position.
All exchanges are subject to risk of hacking but larger exchanges will obviously have more stringent safeguards and may cover losses if they are small in proportion to their overall holdings. Smaller exchanges tend not to cover losses and if significant enough they often end up going out of business. You are better to hold crypto in an offline wallet such as Ledger Nano or Trezor. Some projects supply their own online or offline wallets which could work out better than an exchange but again they are still hackable.