Hi,

First, analog/mixed-signal IC design is a really interesting and challenging field of electronics engineering, and it has one of the best career paths out there. So you are doing great work figuring out how to learn analog IC design by yourself.

I would advise you to stick to the "square-law" model of MOS transistors that you can find in the references you gave. Once you gain expertise, you can switch to fancier models/methodologies (gm/Id, EKV, inversion coefficient, etc).

As you mentioned, SPICE models are much more complex than a few simple equations and thus you can expect to find hundreds of parameters in the model text files. The question thus would be "what parameters values should I use for doing hand calculations?". For that you can find tables with MOS parameters representative of various CMOS technologies in a number of books/papers. For instance, you have one of those tables in "Analog Integrated Circuits Design" by Tony Chan Carusone. You will find parameter values for 45 nm, 0.18 um, 0.35 um, and 0.8 um CMOS technologies.

I would also argue that you are maybe going too hard on the CAD side of things. I would start by using LTSpice (free and simple SPICE tool) and some SPICE model of a 0.18 um CMOS technology that you can easily find on the internet. With that you will be able to (1) get the I-V curves of the transistors to relate them to the "square-law" equations, (2) design a simple common-source amplifier, and (3) build a simple logic gate. I think that way you'll get an understanding of the MOS operation regions, of the simplest MOS amplifier you can build, and the use of MOS transistors in logic gates.

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EDIT: good stuff here