Best sites and practices to disseminate research papers I am thinking of posting a preprint of a paper of mine before I get a response to my submission. This is allowed by several publishers.

I considered three possibilities: arXiv.org, academia.edu and researchgate.net. 

I have a problem with arXiv because it requires posting the source LaTex files which will be made publicly available. I resent this because I am foolish enough to fear that someone may want to plagiarise my work and this would make it easier. In the Why submitting TeX help page they explain why LaTex files are better for archiving but not why it is useful to make them publicly available.

A first question is: is it safe to make the LaTex code public?

Second, do professional mathematicians usually post preprints on these sites?

This leads to another concern. I see that often the results of googling a paper point to the preprints while the published paper is "hidden" in the scholarly article links. Would this be counterproductive in the long run as most people would just download the free version (with possible mistakes) instead of the peer reviewed one?
The website where professional mathematicians share their preprints on in the arXiv.

Regarding your concerns:


Plagiarism is mostly a non-issue. Given the number of articles on the arXiv already, if someone were to pick one to copy, it is unlikely that it is one of yours. Even so, this would not cause any meaningful damage to you.
Many mathematicians actually read the arXiv digest in their particular area, and could notice your article there if relevant for them. Researchgate on the other hand has a somewhat questionable reputation.
You should definitely keep the arXiv version up to date, and fix any mistakes you find there. Many people will indeed read the arXiv version over the one on the publishers website, for a variety of reasons – including not having access to the latter, so you should count that as a plus, not a minus.