How can I research the first recorded usage of a particular sense of a word, especially not the most commonly used sense or most 'basic' sense?

The place to look is in The Oxford English Dictionary, of which there are three editions:

The first two (published in 1933 and 1989) are available in paper and the third one (the most informative and reliable of the three) is available behind a paywall online, though if you can find a public or a university library that subscribes to the third edition, you can see it there free of charge.

Note that the earliest attestation for a word, an idiom, or a meaning is the earliest use of it that the compilers of the dictionary could find. The first known use is almost never the earliest use, which is most often impossible to ascertain.

Consequently, when you see careless writers say that according to The Oxford English Dictionary word X or meaning X arose in such and such a year, they have in all likelihood misunderstood. All the OED is saying is that its compilers could find no use older than the oldest one cited.

You can download this article on the subject free of charge:

"An Aspect of Lexicography Still Not Fully Professionalized: The Search for Antedatings and Postdatings (With Examples Mostly from English and Some from Other Languages" (in Revista Alicantina de Estudios Ingleses. no. 18, 2005, pp. 25-69). https://pdfs.semanticscholar.org/de61/9dcdaa54ad6d819c7b59f62499974253672a.pdf