QUOTE(varst @ Sep 22 2012, 21:45)

Try the Engi ship. Type A, of course (type B is just...what the hell have I tried). Or the Fed Ship.
Sometimes it's all about luck. Rock HW doesn't seem to appear before world 6, and slug HW before world 3. So probably need to pick the central path and see if you're lucky enough.
Rock homeworld can spawn as the 5th world but it's very rare, 7th is far more common
Slug I'm reasonably sure cannot be before 4th or 5th, I forget which now
Getting new ships is far more tolerable with long range scanners, or better yet getting a full map of the sector early on because the quest marker can only spawn in specific jumps
I didn't take note of the zoltan, rock or slug ones as I go those by accident, but the stealth and mantis ones I did.
Neither can spawn in:
an environmental hazard (asteroid, sun, plasma)
a nebulae of any description
a distress beacon
a shop (obviously)
mantis will always spawn in a "ship detected" warning, while stealth is never in a ship detected warning. So if you have the engie/mantis homeworld and long range scanners or a full sector map, just aim for all the systems that match that description (typically 5 to 9 of them) and you're almost sure to find the quest marker. Just don't forget to also meet the other requirements too like having an engi for the stealth ship.
As for the crystalline ship I still need it and the requirements are still hard despite knowing more or less exactly what the game's data says on the matter.
Going by memory:
1. Pod cannot spawn in the 1st sector
2. Pod is an average 1 in 9 chance from any distress beacon in a rock, pirate or engi controlled sector
Pirate - 1/8
Rock - 1/9
Engie - 1/10
3. Odds of getting the pod if you find the event are either 66% or 50% with any random ship, with a blue 100% chance event for the rock ship
4. With the pod, find any Zoltan controlled sector and visit every system that does not have any of the following in it:
an environmental hazard
a nebulae
a distress beacon
a shop
a "ship detected" warning
for a 1 in 8 chance of getting the Zoltan research center event
5. Once you have your new crew, head in the direction of the rock homeworld (very rarely 5th, sometimes 6th, usually 7th sector) to find a brief quest marker shortly before the rock homeworld
6. Finally there should be a quest marker in the rock homeworld itself that unlocks the crystalline cruiser, if you're using the rock ship at this point, you will also unlock one of its 3 achievements
Personal recommended best ships list for the job:
1. Stealth cruiser "type B"
2. Rock cruiser "type B"
3. Any ship you can find a long range scanners augmentation for
Odds might be off slightly for one or two parts there but that's the general gist of it. Doesn't really help me, my luck's been shit since I randomly stumbled upon the Zoltan, Slug and Rock cruisers entirely by accident <.<