Which wallets are the best for keeping a wide variety of altcoins?
I think I can recommend to you myetherwallet.com for your altcoins that are on the Ethereum blockchain. There is no problem with myetherwallet because they are not an online wallet that is holding all your private keys and passwords. With myetherwallet, you have your private key, password, and a JSON file which you can keep all by yourself.
Same here. I'm using myetherwallet with ledger nano s to put more security on mew. As all of my tokens are erc20 based I can store all of them in my mew address which is very easy to use it. Only thing you need is a secure computer and secure internet to access.