I would pick Gridcoin (GRC), as it is one of the more interesting coins out there.

Gridcoin (GRC) replaces mining with doing research for scientific projects, for example to cure Ebola (http://www.worldcommunitygrid.org/research/oet1/overview.do), fold proteins (https://boinc.bakerlab.org/) or find aliens (http://setiathome.ssl.berkeley.edu/).

From a user's point of view, he simply has to run simulations from the different projects using the BOINC software (http://boinc.berkeley.edu/). Then the network comes to a consensus, who has contributed how much computing power to BOINC, which can bee seen for example here (http://www.gridresearchcorp.com/gridcoin/?result&t=CPID_Leaderboard). In some blocks this consenus is saved in the blockchain and the reward one gets when staking a block is proportional to how much research was recently done for BOINC by this researcher.

Setting it all up has been quite complicated in the past, but the pool on pool.gridcoin.co has made alle this easier and already has more than 800 active miners/researchers (http://pool.gridcoin.co/rankings)

I also has very active development, here is the main forum: https://cryptocointalk.com/forum/464-gridcoin-grc/
More information and tutorial to set it up here: www.gridcoin.us
 If you are interested visit our IRC: https://kiwiirc.com/client/irc.freenode.net:6667/#gridcoin