Most of my token stored at MyEtherWallet and once I need it to convert to fiat, I transfer my token to my exchange account. There is instance my token is directly stored to my exchange account to avoid transaction fee. Storing your token is always depends on you and what will you choose wallet as long as your token is secure there is no question what wallet you will choose.
what if that exchange hacked ? you will loss all the money that you collected.
Dont be depend on one thing , distribute your money in multiple wallets and invest equally in all platforms.
I Use meta-mask google chrome extension. To access tokens i use this website https://etherscan.io/address/*****
To transfer tokens i use this website or trading https://forkdelta.github.io