Hello
in the analog design you must pass the hand calculation, even these and specially for the deep submicron will be far from what you calculate, nevertheless it will be in the same direction, if you dont understand the hand calculation then you will not know how to modify your circuit when you simulate it. in addition the hand calculated values will put you nearer to the solution but not the exact. the different is coming from the fact that during the hand calculation we are dealing with very simplifies equation while in the simulator the model is more complicated and includes much more factors that we doesnt take with our calculation.
the first thing in the design is to choose the minimum length which is equal to at least 2*minimum technology length to reduce the channel length modulation and enhance the circuit impedance and gain.
for your case of two stage op-amp I would highly recommend you to use the book of CMOS analog circuit design by Allen and Holberg, in chapter 6 he gave a complete procedure not only for the two stages but for other types as well op-amp topologies.
read that chapter and if you didnt understand it you can message me or post here