This is a follow up from my other question. The answers in the linked question agreed that Putin's incentives for endorsing Trump were primarily domestic, such as pushing anti-U.S. government propaganda in Russia. Are there more details on this? What other kinds of benefits could Putin expect to arise in the short/long run in his own country as a result of the endorsement?
There is a wide variety of benefits
Trump is quite popular in Russia.
According to YouGov poll, Trump has 20% margin over Clinton in popularity in Russia.
Endorsing someone your people like is definitely a positive for your own image.
Clinton is quite unpopular in Russia.
Not just as a competitor to Trump, but in general. She's viewed both as
Bill Clinton's wife (and Clinton is quite unpopular due to both his attacks on Serbia, and perception that he was in charge of breaking-up USSR in 1993 and subsequent major economic upheaval that Russians squarely blame on the West).
AND at the same time she's even more unpopular because she's Obama's SecState; and Russians hate Obama with a passion of a thousand KKK Grand Dragons (reading racist comments in Russian on youtube is quite... enlightening, if I may use such a term).
While I have no evidence to support that, the fact that she's a woman might not help her either. Russians are rather less supportive of feminism than Americans, overall, by extremely large margins.
Most of Western elites hate Trump.
Anything that gets Western elites' panties in a twist plays well with Russians. This is why they are very supportive of Putin being buddies with Al-Assad - they have no particular deep meaningful feelings of brotherhood with a despot who dozes his own subjects with chemical weapons, or deep abiding love of Syria. But they like that helping Al-Assad sticks it to the West.
Putin keeps up his decisive image. Not like other waffling world leaders, afraid of endorsing anyone.
It's a win-win situation for him, where he hedged his bet smartly.
If Trump loses, he gets a "better for Putin" President, as far as US policy goes. If Trump wins, he looks like a prescient leader, in addition to looking decisive.
I believe it's only your own propaganda which makes you think that Putin (or Russia, or whatever) does actually support Trump. As far as I remember Russian media never supported a single US President candidate for years.
Russian press is always something between negative and neutral. Yes, Trump is much closer to "neutrality" than Clinton, but it's not a sign of support of any kind. That rather shows that Trump is not taken seriously as possible next POTUS. And critics of Clinton is rather a preparation for the next step of continuing "cold war". But in unlikely case that Trump will be elected, it will take only few weeks to start criticising him in Russian media.
And considering real benefits of electing one of them, I think that Putin is already much pleased, because both Trump and Clinton seem to be more promising for Russia than Obama himself. They both are equally incompetent, short-sighted and reckless. That's exactly what Putin looks forward to.
In short: Trump election gives Putin a chance to get back to business as usual - adapt his ugly and ineffective chain of command to Putin's and his circle needs and resume pumping of assets abroad. It would stabilize the system which seems to be under stress. Check this is out as an example: http://www.bbc.com/news/world-europe-37058751
If Trump is elected than most likely Ukraine will not get modern weapons. You could get to this conclusion based on Trump statements on Russia in general and on Russia-Ukraine conflict.
If Clinton is elected then it is not entirely clear what would happen with weapons for Ukraine and also with Syria no-fly zone. Clinton was calling Putin as Hitler which is the same as call Obama to be Bin Laden, so it may not be too much field for personal diplomacy. General hawk position of Clinton may resurrect whole bunch of frozen conflicts in exUSSR.
Some possibly well-informed people put this concerns in short form: Clinton election would trigger WWIII or at least CWII: http://www.realclearpolitics.com/video/2016/07/30/russia_expert_stephen_cohen_trump_wants_to_stop_the_new_cold_war_but_the_america_media_just_doesnt_understand.html If you would follow such logic than only one reasonable and effective thing Putin can do is resumption of nuclear tests at full scale. It will put backstop on possible escalations by Clinton administration.
It looks like now that Trump election would allow Putin to avoid making such or similar drastic decisions. Locally for Russia it would mean more international cooperation which is used by Putin and his circle for personal enrichment. Even more international isolation is quite possible if Clinton is elected - quite unpleasant scenario for Russia's elite.