A few extra details left out by Balance:
Gordon has a Ph.D. in theoretical physics from M.I.T, something that is mentioned again in the second chapter of HL2.
The Marines aren’t the ones in black. The Marine special forces were getting their asses handed to them by the Xen aliens (who put up a much fiercer resistance than the lab-coated unarmed scientists), so someone called in the ninja-like female Black Ops. It is never established in HL1 who the Black Ops work for, but just as the marines were sent in to kill all survivors, alien and human, their failure results in the Black Ops being sent in to kill everybody, including the marines.
The vortigaunts were slaves to whoever was controlling the aliens. All slave aliens have metal wristbands that seem to act as some sort of shackle. The final boss of Half-life also had similar wristbands, implying that although he was keeping the portal open, he was doing so at the behest of someone else. In HL2, Gordon’s defeat of the alien bosses from HL1 allowed the vortigaunts to escape the bonds of slavery, and they joined the human resistance against the combine invasion.
Dr. Breen, who was only referred to as “the administrator” in HL1 (a title originally attributed to the G-Man up until HL2 indicated otherwise), struck a deal with the combine before the events of HL2 but after the events of HL1 to turn Earth over to them. This avoided a war, but essentially made humanity slaves to the combine. The obvious connection here is that it was quite possibly the combine responsible for the conquering of Xen and some of its aliens being enslaved.
The G-Man seems to be working against the combine, which is why he pulls Gordon out of stasis, but there’s nothing to indicate he has Gordon’s or Humanity’s best interests in mind. His “employers”, as he calls them in HL1, seem to be calling the shots with Gordon, but who they are is undetermined.
HL2, while having an interesting premise, answers hardly any mysteries from HL1, and creates a whole bunch more. From what I understand, the Episodes (which I’ve yet to play) resolve a decent amount. I haven’t heard if HL2: Episode 3 is going to wind everything up, or if HL3 is supposed to do that.