Use myetherwallet to store your erc20 tokens, it allos almost all tokens from ICO's, and it is very easy to use, i use to store all my coins in there, and it works perfectly, i can manage my money very easily, i sugest it to you.
Or just hold some part of your coins on bittrex as you just said, but maybe it is a little bit risky, maybe one day you would be hacked and you will probably lost your money, so better to store all your coins on myetherwallet.