To answer the question whether you should or shouldn't invest in it, please read my recent (and first) post on Steemit: https://steemit.com/eos/@chencho777/how-will-eos-token-price-evolve-over-time-is-it-sustainable

TL;DR: don't invest now, IMHO the price is not sustainable at current levels. Wait some weeks and buy cheap EOS tokens once the hype has passed. And in a year's time, when this endless ICO is over, the price will probably rocket without the downward pressure of a permanently open ICO, avid of daily ETH in order to sustain the price at market levels.

Currently you can store them on a regular Ethereum wallet with ERC20 token support (such as MyEtherWallet). Once the ICO is over, assets must be transferred to the native EOS network, otherwise they will be frozen forever (and they will only give you 48 hours to do that from the last day of the ICO).