Trump said a lot of that stuff during the campaign because he likely hadn't realized the extent of the proxy wars between the US and Russia since the wall came down.
One of the main reasons the US invaded Iraq was to do so before Russia took control of the region, due to its importance to the oil supply. Russia had good relations with Saddam's regime and with Iran. When Saddam was overthrown, many of the oil industry spoils that had been going to Russian firms were redistributed to US (or coalition) firms.
Russia is currently helping to stoke discord in Syria and aligning with Iran mainly to force an over-stretched US to react. For pennies on the dollar Putin can keep the US in a middle-east quagmire, so why not do this indefinitely?
Trump may not have realized the strategic purpose that US escalation in Syria was intended to achieve, he may have believed the PR that we were involved for humanitarian reasons, etc. But he seems to have concluded that it was a money pit waiting to happen with little humanitarian upside (which is a correct conclusion, and the conclusion Russia had hoped the US would draw). HRC was determined to signal the opposite so that Russia might stop spending its pennies there.
For those who don't realize this, the decades-long Iran/Iraq war was a proxy war fought between the US and the Soviet Union with both sides having the goal of creating a dominant footprint in the middle east to keep the other side at bay and guarantee the relative stability of oil extraction. This same goal also causes the US to act to prevent any sort of large scale democratic movements in the middle-east; Al Qaida began as that exact sort of pan-Arab movement.
So if Trump is proposing a negotiated deal with Putin involving Syria and Iran, that means he's willing to consider dividing the spoils in a way that may harm US coalition allies (France, Germany, etc.) who also have firms that are heavily invested in post-Saddam Iraq and some of which would likely be displaced by a new US/Russia agreement.
Similarly, allies of the US in Europe that fear an emboldened Russia also stand to lose if Russia gains better access to cheap petroleum. Russia, on the other hand, is poised to take a big leap forward in economic output and also reputation laundering. A successful negotiation with Trump could wipe away the penalties/sanctions that Russia has faced due to Putin's brutal approach to certain domestic issues.
So Russia's goal has been a larger presence in the middle east, a laundered reputation, and possibly more (everyone fears it will attempt to re-annex more former Soviet territory).
The thing that I think HRC and Obama misunderstood is that Russia is very likely to get this whether the US wishes it to happen or not. The US (and allies) are not in a position to undertake preemptive strikes, and so all they can do is vilify Putin and create a massive PR campaign and pressure allies into sanctions, etc. Meanwhile, the US can use clandestine operations to help goad Putin into various crackdowns or overreaches that will force him to act more like a dictator and increase the chances he will be unseated due to domestic dissent.
Why didn't Obama intervene in the Caucuses or the Ukraine? Because the US does not have the will to enter into conflicts like those, and certainly does not have the will to risk nuclear conflict.
Posturing by McCain about both annexations was nothing more than a bluff, as was HRC's sudden tough talk toward the end of the campaign. The hope was that somehow Putin would fall for this bluff and that rabid anti-Russian public opinion in the US would scare Putin into thinking the US might react with force.
Seriously, this isn't going to happen no matter who is president. The question is how long it takes and how many lives are lost in proxy wars before Russia occupies a position of greater dominance in Europe. The Soviet Union was too big and plagued by infrastructure problems, but Russia itself is well placed geopolitically and has historically been a seat of wealth, culture, and regional ambitions.
What is in the best interest of the US with respect to the negotiations (hard or soft) that take place with Russia over the next decade? I'm not sure. But Obama (and Trump also) saw that there was a certain inevitability to it and that it was not worth spilling too much blood over. In spite of this, Obama carried on proxy wars in Iraq and Syria which killed hundreds of thousands of people and caused untold suffering.
Trump has claimed that he may not wish to continue the proxy wars. We should all be relieved. Rather than debating rumors about Russian meddling, etc., we should figure out what is actually in US best interest over the medium to long term and negotiate accordingly. Bluffing isn't going to work. Both Russia and the US are willing to let lots of people die in proxy wars, but neither is willing to engage in direct conflict, so we will either inflict another decade of tragedy upon the victims of our proxy wars, or we will find a less violent equilibrium.