I think you can log in after some time passes if certain conditions don't occur in the meantime. After x amount of time the game will find countries and close them if they have been inactive for so long, or so I've read. Also a certain amount of debt will result in a country closing as well.
If you haven't reached a maximum game level to receive gc awards on White Giant world I wouldn't be so fast to expand. But if you get some level awards and are tempted to expand, I would go to LU. LU allows you to make money faster that can pay for your empire faster than any other world. If you focus on being profitable in the game it is very possible all your expansions will earn enough coins to pay 30 coins a month. It is even more likely that an LU empire could net you enough gold coins in order to pay for several worlds. But it won't happen overnight.