This is an entirely subjective ranking, based only on one person's opinion. This page does not have any affiliate links nor any other input from the exchanges listed.
There are hundreds of exchanges, and citizens of the U.S., North Korea and Iran are prohibited from using many or most of them, including the top two global exchanges Binance and Huobi. This page will only list a few exchanges.
All U.S. exchanges are heavily regulated by the U.S. government and defer to the U.S. government on all issues. If you buy a coin on a U.S. exchange and the U.S. government tells exchanges to remove that coin, even if it is on a whim, the exchanges comply immediately. Same story in most countries. Coin listing disputes are often political, the 'Tether' controversy was a good example. the United States determines which coins are liquid and which are not. Namecoin is the best example.
Some regulatory activity is genuinely intended to 'protect' consumers, but much is political gaming by the countries involved. When Bitcoin first pumped in 2013 Chinese regulators got a reputation for manipulating markets. They would announce a ban on bitcoin, the price would drop and a massive number of bitcoin would shift to Chinese exchanges, then they would 'clarify' that it wasn't a ban, and the price would jump. The U.S. started playing similar games a few years after. Because of 'hard to define' connections between bitcoin and the U.S. government, the bigger picture is hard to decypher.
Coinbase is obviously the easiest exchange to use for an absolute beginner. Once a person learns a bit then they can open a CoinbasePro account and trade more currencies. The corporate entity behind Coinbase may be heavy on politics but it is a generally fair exchange for U.S. citizens, people in other countries should be cautious obviously. Very simple interface. Should be noted that when Coinbase started they did not report volume publicly for a long time, to hide their low volume, and even today there are indications that depth on their exchange is not quite as solid as it looks. They are fully regulated though, have massive reserves, and are not a risky exchange. their early volume games point to their leadership using muscle and manipulation to cover up incompetence which does not bode well long term.
Bittrex is a decent exchange with a lot of coins. The restrict various coins depending on your location, but they have a lot of small coins you won't find easily elsewhere.
Freiexchange is probably the best exchange to find old coins that might have a chance of appreciating a lot. They are also one of the few, or perhaps the only, exchange that does not list coins based solely on popularity. They do not list Ethereum, Monero, BSV and other 'large but dubious' coins which are listed on every other exchange in the world, despite having a chance to increase their volume by doing so. The exchange was initially made to allow one old coin, Freicoin, to be traded. A very up front and straightforward, honest exchange, but very low volume.
QTrade is another small exchange that says it is based in the U.S.
Yobit is an old Russian exchange that also has a lot of old coins. A reliable exchange but very commercial. Not responsive to foreign pressure so it lists coins other exchanges are afraid will lead to U.S. pressure.
Kucoin is one of the biggest global exchanges and does not explicitly ban U.S. citizens at this point. They have a lot of coins, high volume, and are a good exchange, largely modeled after Bitfinex.
Poloniex used to be perhaps the best U.S. exchange, until they banned U.S. citizens.
BitStamp is one of the oldest crypto exchanges and still accepts U.S. citizens.
Gemini, Kraken, LedgerX all cater to mainstream U.S. users. Very mainstream leadership, corporate cutouts trying to play crypto.
Keep in mind that if public key cryptography is secretly broken, and that is likely, any exchange is vulnerable to a hack by government actors at any time. Contrary to public belief, it is not the North Korean nor Iranian governments which do most hacking of that sort.
Decentralized exchanges will be the best option soon, as long as a person does their research. Make sure you are buying the coin you believe you are buying. Always withdraw immediately to your own wallet. Divide your purchase into smaller units in case your coins disappear at some point in the transaction.