Personally, I've always liked creating a simple web server as a nice step in learning a language/stdlib. Some concurrency, some I/O, some string parsing, etc. Obviously it's not the first thing one does, but I find it a nice package to put together that actually achieves something real.
Thats a fantastic idea for a decent sized project that will expose you to many aspects of the language and tools commonly used with the language. I'm going to include that one in the list.
couple of days back i started with writing a TFTP client+server program in erlang. the protocol is 'trivial' enough (to not get bogged down in complicated fsm's etc.) and still provides sufficient 'meat' to exercise core language features etc.
it is still going on, but is definitely great fun...
The really tough part of picking a new language is learning the idioms.
If I handed you a book describing the French grammar and an English to French dictionary and told you to write some short stories, you might be able to put together something parseable by a Frenchman but you wouldn't be writing French.
I don't pretend to have a good answer except reading and modifying other people's code seems to help.
