You can use myetherwallet and wavedex.for erc20 coin you can use myetherwallet and for waves based coin use waves wallet. don't use a exchanger wallet for storing your coin.its high risky also.anytime exchange platform can be hacked by hacker.
I totally agree with you, when you buy alts just store them in your desktop wallet or a trusted online wallet like myetherwallet and when you want to trade just send the amount you will use to exchange wallet after making the profit you wanted withdraw it back to your wallet that you and you only know the private key.
This is what I do generally and every thing is going well till now.