Preparing lecture notes and references?

There are three different sorts of bibliographic entries in your situation, I think: suggestions for further reading (for the students), acknowledgement of your sources, and historical references. One should acknowledge one's sources, whether or not it "helps the students". I think it will help them in the larger sense of perhaps slightly better appreciating how human knowledge is advanced and organized. Including historical references helps people understand the timescale on which things happen.

Even with "well-known" relatively elementary results whose origins have faded into obscurity, you can note that you learned these things from various textbooks yourself... not that you came up with it all yourself, for example. You could tell the textbooks you studied from.

Even if that information is not "tested-on", I think it sets a good model for the students.

I suggest putting attributions in-line, as pointers to a "References" section using whatever citation format your institution generally uses, and providing a separate "Reading List" which may include material also attributed in the notes.

There’s nothing preventing you from compiling two entirely separate bibliographies, under separate section headers: One with highlights/seminal works (“these are worth skimming”), and one detailed bibliography for individual claims and sources.

A few popular science books and textbooks do that and it’s a huge benefit to the reader: if you managed to stir the students’ interest, many will peruse the reading list out of curiosity. By contrast, few (if any) will read through the detailed bibliography (who even does that?) but if somebody needs to follow up on an individual reference, it’s there.