If you do hold up lots of coins then local wallet would be suggested but there are still some online wallet which are good too since you can able to get its p.key which is good as long you do have it you do have always the access into your coins.Never ever store huge amounts on those wallets that you don't have its key.As most people suggested here local wallet is always been good. There are respective wallets of a certain coin depending on which platform that they are using.