Speaking of the Borg, time travel may confuse first contact with the Borg a bit but I'm going to go with the episode "Q Who" as the official contact made between the Federation and the Borg. It all begins with Q, who whisks Captain Picard away in order to get him to promise to give a request that he has a full hearing. It turns out Q wants to join the crew, but Picard denies him and insists they are ready for anything when Q says they'll need him for what's out there.

Angry, Q takes the ship 7,000 light years away to force them to see what they'll face and how they'll need him. Guinan knows this area and tells Picard they should start back now but, being the explorers they are, they look around a bit and find themselves faced with a Borg cube. Picard tries to communicate with it to no avail and Geordi is the first to see one when it beams into Engineering. Seeing what it's doing, they try to neutralize it and soon discover how strong the Borg are and how they can adapt.

Riker takes a team onto the cube to learn more and it's the start of them becoming familiar with the Borg that would continue to haunt the Enterprise and Federation for years to come! In the end, Picard has to admit to Q they need him to escape and Q does return them to where they started. However, they all know this won't be the last time they face the Borg.

It's a memorable first contact for so many reasons, beyond the Borg just becoming such an iconic Star Trek nemesis. It's fascinating to see how Picard and the others react to the species. They consider all the angles, investigate and have to adapt themselves when everything they try fails. It's also a deadly interaction in that the Enterprise loses 18 people as it goes through this process.