Store them in the my ether wallet. You can send any kind of coins or tokens there. If you dont find your coin or token there then can add it manually. You can hit the add custom button at the right down side of my ether wallet. The reason you should keep your coins on mew is because you can hold the private keys of mew which means it is in full control of your own. In any case nobody will be able to access the assets that you hold and not even mew themselves.
Thanks
Some of them are ethereum based ERC20 tokens. You can keep them in myetherwallet. For the others i advise you to install their own wallet announced in their official websites. Do not keep them in exchanges. Exchanges are always risky.
Does every altcoin has their own wallet?
Whatever you do don't buy WINGS. I own some and let me tell you: it's a complete piece of shit.
Could you elaborate more about wings?