C560 First Officer reported while cleared for a visual approach not aligning to the correct runway and descending below a safe altitude resulting in flight towards terrain. ATC climbed and vectored the aircraft for another approach.

Narrative

We were cleared for the visual approach to RWY XX L at ZZZ. I reported the runway in sight; and the Captain (pilot monitoring) concurred. We accepted the clearance. The ILS was not armed for backup; which in hindsight would have provided additional situational awareness. I was the pilot flying at 3000 feet. The Captain instructed me to descend to 1500 feet. I felt we were still too far out and not aligned; I asked if we should hold altitude longer. The Captain responded; 'we are visual;' so I began descending to 1500 feet.During the descent; I identified a runway directly ahead and assumed it was RWY XX L. We later realized it was not the correct runway alignment. ATC intervened; advising us that we were lining up incorrectly; and instructed a climb to 1600 feet; then to 3000 feet; with a right turn to heading 090.I initiated the go-around by adding power; and at that point we transferred control -- the Captain became pilot flying; and I handled radios. Initially; the Captain began turning left; but I called out 'Right turn 090;' and ATC simultaneously re-issued 'Right turn 090.' The Captain corrected to the right.During the climb; we briefly exceeded 3000 feet before descending immediately back to the assigned altitude. ATC then provided radar vectors; and we subsequently performed a normal approach and landing to RWY XX L without further issues.Suggestions: Looking back; I think this event really showed how important it is to back up a visual with instruments. Even if ATC clears us for a visual; having the ILS armed or the FMS extended centerline displayed would give us that extra layer of awareness and make it harder to misidentify a runway. I also feel CRM plays a big role -- if one pilot has doubts about the timing of a descent or alignment; it should be encouraged to speak up and hold off until both are confident. Finally; when operating around airports that have multiple nearby runways; it would help to make a point in the briefing to call out those surrounding fields so the whole crew is aware and less likely to confuse them.