I must agree that the documentation is a bit terse but the tutorial gets you up and running quickly.
http://twistedmatrix.com/projects/core/documentation/howto/tutorial/index.html
The event-based programming paradigm of Twisted and it's defereds might be a bit weird at the start (was for me) but it is worth the learning curve.
You'll get up and running doing much more complex stuff more quickly than if you were to write your own framework and it would also mean one less thing to bug hunt as Twisted is very much production proven.
I don't really know of another framework that can offer as much as Twisted can, so my vote would definitely go for Twisted even if the docs aren't for the faint of heart.
I agree with Greg that SocketServer is a nice middle ground but depending on the target audience of your application and the design of it you might have some nice stuff to look forward to in Twisted (the PerspectiveBroker which is very useful comes to mind - http://twistedmatrix.com/projects/core/documentation/howto/pb-intro.html)