I see a lot of people having issues with exchanges holding their coins. I have looked up and there are a good amount of places to buy ada.
How I buy ada is getting ethereum on coinbase and then using COINSWITCH. it works buy me sending ethereum to coinswitch and then it sends the coin to the wallet address you put in so it never stays on an exchange and it is all done in one fell swoop.
Edit. of course buy a little first to make sure it gets sent to your wallet and not a fake coinswitch site ( do this for all new wallets and exchanges you use!) once its confirmed in your wallet bookmark the site!
use crypto converter to make sure you are sending the right amount (it tells you how much one crypto or fiat is to one another and has always helped me make sure im sending the right amount that I want especially using multiple decimals)