Advice on Wallets- Wallets for multiple Altcoins?

I am new to the world of cryptocurrency. I have recently invested in ETH on coinbase. I hope to invest in other altcoins soon.

My question is, is there a wallet that you can transfer from coinbase to store your cyrptocurrencies off that exchange, that will facilitate holding various different altcoins in the one wallet? (for example could i set up a wallet that holds Ethereum, Monero, Bitshares and Dogecoin all in the one wallet?

If so, what are the best recommended wallets to use?