You can use a few popular websites to buy bitcoins using FIAT currency and then you can use exchanges to buy any altcoins with Bitcoins.
- cex.io - Immediate buying option with limits. Limits increase after approval. Can buy with Credit Cards.
- xcoins.io - Can buy with Paypal.
- Bitshares - Decentralised exchange with more currencies being added to exchange.
- changelly - Seems to be popular.
I am using all of these and will add more notes as I go forward. If you are from India and have used any of these or better websites do let me know in the comments. I would like to try them out.
If you are from US you can try
- CoinBase - Popular and easy to use.
If you are from India checkout https://steemit.com/bitcoins/@gokulnk/how-to-buy-bitcoins-in-india