In the introduction to my thesis, I cite a lot of classical results from the 19th and early 20th century. Should I try and cite the original source for these results, or does that look like I am trying to bloat my list of references to look smart and I should rather find a good monograph/survey on the topic? If I do go with the second option though, does it suffice to mention the book at some point in the beginning and then say things like "Bernstein showed" pages later without further citing a reference for where or when Bernstein showed that? It feels wrong to have "Bernstein [1] showed" when [1] is not by Bernstein.
(One answer could be: I cite where I have it from. But those classical things I read mostly on Wikipedia or in lecture notes and then go and look for appropriate sources)
Your question is important. My answer is that it really depends on the nature of the item you are writing (I know you are writing a thesis, but let's forget about this for a while).
If you are writing a book, then you should try to cite the original source. Although really old papers are hardly accessible in an easy way, the author of a book should always point out to the reader who proved an important result for the first time, and possibly where the reader can read the first proof.
If you are writing a research paper, then a recent textbook where statements and proofs in contemporary language can be found is more helpful than old-fashioned manuscripts. Accessibility is really important to those who study a new research paper, and if you cite a book from 1902 that nobody will ever manage to read, then you will be criticized.
My opinion is that a thesis (master thesis? Ph.D. thesis?) is closer to a book than to a research paper, and my advice to you is to cite the original sources as much as you can. This is just my humble opinion, anyway.