He was thinking about Binance, and it's of course a good exchange, but it seems that they have strict KYC policies and their terms allow them to share personal data of their users with too many entities (like, not just the authorities, but also companies that want to promote some products, it's crazy!).
I can't think of any other good exchange other than Binance and in fact, you can use their full service without turning in your personal documents unless you are a heavy trader which makes your withdrawal exceeds 2 BTC limit per day.
Alternatively, you can also try
Bitfinex with 10 BTC withdrawal limit per day; if it exceeds, then you are required to undergo KYC as well.
I am not a trader but I think it will not hurt if I just observe these exchange scam accusation before they ruined numerous traders lives.
[1]
HitBTC Scammers Face Two Years in Jail for $140K Bitcoin Twitter Fraud[2]
HitBTC Review and ComparisonOP is talking about a beginner trader so I assume giving Binance a try with $20 should not be that harmful. Bitfinex is also a good one. He would better take a look on policies related to his country in each exchanges and everything should be fine.