Infinity factions work by having an overarching main faction, and then sub factions ("sectorials") that have more of a particular flavor of unit, but less overall variety. You can take either but not both at army creation, it just affects how many and of what you can take. Corregedor is one of the sub-factions of nomads (and incidentally, one that can in fact take an Iguana), and tends to have lots of the "*cats" units, lots of engineers and the like, though
IIRC, they don't get the really heavy hitter hackers. If I'm remembering right, everything on your list you like is Corregedor, except the
REM which is pretty much shared across all Nomads, Corregedor included, so either pack would work just fine, depending on which models you like more. Likewise, fluff wise subfactions will work with the main faction (rather obviously), so if you try corregedor and decide you'd rather try for say, Szalamandras, Interventors, and a Morlock group instead, you can just use some of them with those models as a generic Nomads list.
Also, to play around with,
Aleph Toolbox, and the army creator on the Infinity website are great for figuring out what'll fit and what you can take faction wise in an army.
Edit: probably should step back one step: the two starter boxes link to the above by one having units across several sectorials as part of a united Nomads force, while the Corregedor one is just Corregedor units, for if you want to go sectorial (or just like the units in it as part of general nomads).