Other crystal manufacturers also have piles of documentation on the stuff, so feel free to dig through their lit. Pragmatically, I think short checkoff lists of no-no's goes something like:
1) is it an overtone crystal - most uC osc's won't work (properly) with overtone crystals.
2) serial/parallel resonance - I think pretty much everything is parallel for non RF stuff.
3) load capacitance - follow whatever the manufacturer specifies, tune for PCB layout, and pin capacitances.
4) power limits - crystals are rated for power dissipation (microWatts...). The uC datasheet will recommend the minimum power dissipation required.
5) accuracy requirements - if 200ppm isn't good enough, you'll need to read the fine print - especially with respect to temperature coefs.
6) oscillator requirements - with typical CMOS oscillators (i.e. a tuned inverter), a feedback resistor of ~1MOhm is required to bias the inverter into it's linear region. Sometimes this is built in, so read the docs on the oscillator - i.e. the uC docs.
I think the majority of the details about "cuts" primarily affect the load capacitance and the temperature coeffecients. Unless you are doing a clock/timing application, it shouldn't matter.