BAY is a decentralized marketplace intended to allow their users to trade freely with each other. They do this by way of the downloadable client which will enable access to their market. They are not the first, and also likely not the last blockchain project to attempt this.
However, many soon find that getting people to actually switch from using a website to a download client is easier said than done. This project has been ongoing since 2014, with little success in acquiring a user base.
This community project is big on heart, but their marketing leaves much to be desired. If they are ever to establish themselves as an alternative to marketplaces like eBay or Amazon, it will take a much bigger push, and they may not be capable. If you plan to make a BitBay investment, you should be aware that you could be holding for a very long time. Adoption of this scale is not an overnight event.
There are only a tiny number of places where investors can buy BitBay, however, there are a couple popular options here, and the volume is at a decent level to execute a trade. Bitcoin is the only really viable option here, but there is a little bit of trading volume for the Euro, if you'd prefer to use it. Though due to the liquidity distribution, you should be sure that you are not overpaying for the privilege.
In order to store your coins, you'll need to use one of the official wallet options. You have a choice between the downloadable client or a web wallet. They do have options for Android, Mac, Windows or Linux if you'd prefer the download option. In any case, be sure to back up your wallet file or seed for safety.