We did something similar in the past under the XML Gateway.
Depending on your data source (e.g. following applies for filing history lists or streaming API) can you not just use the category
field though e.g. for “incorporation” (e.g. “starting” / “registering in the UK”) the value:
incorporation
… should cover both incorporation and articles? (Unless the filing is really old / obscure / Companies House has otherwise not categorised it “correctly” - although since they are the official “source of truth” ultimately it is up to them!)
One of our use-cases was identifying certain key filings - so in this case we actually were happy to try to limit the search so we only got the “main” filing (and not e.g. resolutions or associated filings) and only fell back on the more obscure things if the “usual” documents were not there.
We do have more general uses though so do need to support the detail. So we still have some routines which check this (if e.g. description
is missing or empty) because of our legacy use of the XML Gateway and “just in case”…
I’m still not sure why you would need to worry about the type
since Companies House clearly want people to avail themselves of their new description
codes here. However - I don’t need to know of course! 
In your case I can’t say exactly how you might decide to categorise something - that depends on the question(s) you want to answer. So in our old list we had some but not all of the forms your listed, and also others you didn’t mention.
For incorporation you might then also note:
NCIN01 Application by a joint stock company for registration as a public company under the Companies Act 2006
Possibly: NCIN03 Application by a company (not being a joint stock company) for registration under the Companies Act 2006
Then there’s … NCIN04 Statement by Director or Secretary on application by a joint stock company for registration as a public company under the Companies Act 2006
Again - I don’t know for sure but I suspect @SmokeAndMirrors first list covers most things.