I have just started with Rindler's Relativity: Special, General and Cosmological (newer book, 2 Ed.). Another book I recently came across is Gabriel Barton's Introduction to the Relativity Principle (Wiley). While I have not seen it listed among the must-reads of relativity literature, I find this book quite useful. I feel the author takes the time to state everything as clearly as possible. He actually uses the light clock to introduce time-dilation, but this is before introducing the LT, and even the in the chapter on LT, he derives them at the last. The case where the frames may not be oriented in standard configuration is dealt with in an appendix. Yet to read the chapters introducing four-vectors, but the chapter on space-time intervals is more or less straightforward - introduce the expression and prove that the interval is an invariant by substituting the Lorentz transformations, classifying intervals, and a couple of examples on space-time diagrams.
I have not read many books on relativity, so I can't really say if this better than other 'standard' ones.