Hello there, what is the best website to buy altcoins?

Coinbase
^ The most noob friendly website. However this site only offers 3 altcoins, Ethereum, Litecoin, and Bitcoin Cash.
I'd advise you to trade your bitcoin on an exchange such as poloniex or Bittrex, which both have a variety of altcoins.
Do note that when using substantial amounts, passport verification is needed, just like coinbase.
Alternatively you can also use cryptopia, if you want to invest in really "unpopular"/new coins. ( Although most of these are either dead, or a pump & dump.)