I did a comprehensive reading order for the series a few years ago, but it consist of the order for the issues, not the trade paperbacks and is quite long. I can give you that if you want, but as for a reading via trades, I can only link to other websites. In any case, here's the [link to the reading order I found on the web](collectededitions.blogspot.com/2011/03/superman-new-krypton-trade-reading.html?m=1), followed by my own reading order which is based on the shield numbering from the original release:
The crossover itself is separated into four major parts. When the books were first coming out, DC returned to the triangle numbering system (in this case, shield numbering) used in the 90s to help readers follow the story between series. For this reading order, I have listed the books by their shield number, followed by the book/issue number assigned to that shield. Some books will not have the shield, but should still be read in the order as listed below. The shield numbers also restart from zero at one point. Luckily, they are color coded. The first set of shields are green, the second is red. When it comes to it, I will list the distinction as having begun.
Preludes: These are recommend reading for events that lead or set up characters and story points that will be touched upon in varying ways in the crossover.
Superman: Last Son - This introduces General Zod, the Phantom Zone Criminals, and Chris Kent.
Superman: The Coming of Atlas - Sets up a few characters, but not really essential (and not all that great, to be honest).
Superman: Brainiac - introduces Brainiac and directly sets up the events of the New Krypton crossover. If no others, I would say this one is the most essential for what's to follow.
Part 1: New Krypton:
Part 2: World Without Superman:
Part 3: World Against Superman: Red Shield numbering begins
Part 4: Last Stand of New Krypton:
Most, if not all of these issues can be found in the following trade paperbacks. Note: I've never read this crossover via trade paperbacks, so I'm not certain of the order in which they should be read, though I'm sure a suggested reading order exists somewhere on the web: