First of all Bitcoin is something different than altcoins. Best Bitcoin web wallet is Blockchain - https://blockchain.info/, with this wallet you can send/receive Bitcoins. Or you can install Bitcoin wallet in your computer, for example, this one - https://multibit.org/. And then you can start to think about altcoins for example, from this site - https://coinmarketcap.com/ - there you can see a lot of altcoins. You will also need altcoin wallet, for sending/receiving altcoins - it depends which altcoins you buy/sale. There are also some multi altcoin Web wallets with instant exchange, like Cryptonator etc.
If OP is planning on buying a bunch of coins, I wouldn't recommend him to use a web wallet to store his bitcoins. Instead OP you can try a desktop wallet like electrum or any of the listed wallet in here: https://bitcoin.org/en/choose-your-walletFor a trading platform, I would suggest bitfinex and poloniex also new coins are mostly being listed in c-cex.
For purchasing bitcoi I think you can try localbitcoin or afaik isn't there an atm machines in your area? You can purchase bitcoin in there too.
