The best wallets are always paper, hardware, and core wallets in terms of security and control. But of course that can not be multiple.
There are many wallets that let’s you store your altcoins and they have very good reputation. Most people store their altcoins on exchanges (I assume you are aware of the risk that exchanges pose) because it’s simple and you can make exchange anytime in addition to storing altcoins.
Following are some of the best wallets trusted and tested by time.
Bittrex
Bitstamp
Holytransaction
Bitpay
Poloniex
Kraken
Exodus
Coinomi
Electrum
Jaxx
Remember that many of the names mentioned are primarily in exchange business and has a daily trade volume of 10+ Million. Please choose carefully.