Zilliqa is a blockchain designed to solve the scalability problems presented in other chains. While many investors thought Ethereum was immune to the transaction clogging issues of Bitcoin they soon found out they were wrong after the Crypto Kitties fiasco. Their platform is capable of transmitting 2.5 ktxs/s verses Ethereum's 7-10 tx/s.
By utilizing something called "sharding" their performance aims to scale with the growth of the network, a serious pain point for cryptocurrency after its massive growth spurt. Their platform also supports Dapps, and they have a proposed fairer mining algorithm in place for miners that will allow individuals to make more money for verifying network transactions. If they succeed, your Zilliqa investment could be a valuable one.
You can buy Zilliqa on several top-level exchanges, but it is notably missing from a few big players which can hurt the overall trading volume of the coin. This token does have the advantage of multiple trading pairs on various exchanges though so if you'd prefer to exchange your Ethereum for it instead of Bitcoin you've got options!
As this is an ERC20 token you can use pretty much any compatible Ethereum wallet to store them as most of these allow for "Ethereum assets" to be stored as well. This can include web wallets like My Ether Wallet or mobile wallets such as Coinomi, which I prefer to use for my assets.