I have at least 6 different altcoins sitting on Bittrex and Binance.
Since I am still pretty new to trading cryptos, I would like some advice on how to keep these coins safe?
It seems there is no wallet which will be able to store all available brands of coins.
So what do you more experienced traders do with lesser known coins, if you cannot find a wallet?
It depends on the altcoins you hold. You better keep every altcoin in its own wallet, I think it will be safer because you can save all your private keys.
Wallets that can hold many altcoins have higher fees and somtimes they don't give you private keys for each altcoin you hold.