I think the most important parameters for an opamp in a LDO are PSRR and offset voltage, since they would directly affect your output accuracy. Open loop gain is also important to have better accuracy. Slew Rate and noise are important according as the specification of your LDO and the reference level.
All of them may be used. Reasons depend on your specifications. DMOS if you need high voltage operation. BJT if you need good accuracy and low offset Opamps. MOS otherwise.
I have just design a LDO same as your figure . But If I upload it , My boss
will .....
So what I may say is , the main constraint on the design is the PSRR of
voltage reference , and the eror amplifier is 1 stage with a buffer ..
nothing is special !
There are many ways you may use for compensation for example:
1. Dominant Pole Compensation
2. Gain Compensation
3. Lead Compensation
4. Lag-Lead Compensation