The monero team recently ran a hardfork (April 5th I believe) to keep the mining difficulty low with the new asic miners that were recently on preorder. One of the leading coins in privacy if not the lead. Ricardo Spagni, aka fluffypony, is one of the lead developers who is very public about the advancement and development of blockchain technology. There is a mobile wallet, monerujo that is free and easy to use. Also you can store them on a computer if you download the monero chain. The client has a pretty interesting interface. It does take quite a while to download and takes up quite a bit of space, but it is an alternative to keeping monero on an exchange.