Well, they'd have to choose a totally different altcoin exchange to the fiat-related exchange that they chose.

For fiat, I suppose a newbie could try Coinbase or Bitstamp.  They do have KYC procedures but as time goes on that's going to be more and more necessary - it might make sense to start now.  If they really value their privacy though, they could go for something P2P like LocalBitcoins.

For an altcoin exchange, there's no one reliable exchange and all of them have a lot of complaints.  But the closest thing to a reliable exchange that I've used has been Bittrex.