First you should install a wallet dedicated for the cryptocurrency you want to buy, for example you want to invest in Bitcoin, you need to have a Bitcoin wallet like electrum or buy a hardware wallet to secure your Bitcoins and have a full control of it and you can also store other cryptocurrency in hardware wallets, just make sure to check if the coin you want to buy is supported by the hardware wallet you have. You can buy cryptocurrencies in exchanges like coinbase, localbitcoins, bittrex, poloniex, binance, etc. For beginners it is recommended to try to invest first in Bitcoin, but as a newbie you should first understand everything you need to know about cryptocurrency and decide later on which coin you want to trust.