Little tip, start it with
screen bitcoind
You can then exit the session and leave it running.
Just created a droplet myself. tried it on CentOS first but had trouble so tried Ubuntu and it worked first time.
{
"version" : 80500,
"protocolversion" : 70001,
"walletversion" : 60000,
"balance" : 0.00000000,
"blocks" : 108023,
"timeoffset" : -1,
"connections" : 8,
"proxy" : "",
"difficulty" : 25997.87992881,
"testnet" : false,
"keypoololdest" : 1386955780,
"keypoolsize" : 101,
"paytxfee" : 0.00000000,
"errors" : ""
}