First thing is you should have a public address when you created your wallet. The public address is basically your account number and the private key is what opens it, so you need to keep the private key to yourself. Secondly you can only send bitcoins to bitcoin wallets, and ethereum to ethereum wallets, etc. So don't mix the wallets (except ERC-20 tokens, which will go into ETH wallet). So USD to USD wallet in coinbase, Bitcoin to Bitcoin wallet in coinbase, ETH to ETH wallet in coinbase, etc. Never ever send a different type of coin to a different type of wallet, you will most likely lose it forever!
With Coinbase, you transfer USD from your bank account/credit card to your USD wallet in Coinbase. From there you can purchase, BTC, ETH, LTC, BCH. Once you have these you can transfer them to your personal wallet of the same type if you wish. To buy Altcoins, you'll need to transfer one of the four coins mentioned to an exchange such as Binance, Bitterex, Kucoin, etc. (recommend ETH). In these exchanges you can trade the coins for other altcoins. The exchange trade in pairs.( example, if you tranfer ETH to binance, and you want to buy NEO, you choose the ETH/NEO pair.) Good Luck I hope this helps.