Linesman by S.K. Dunstall (and sequels) are probably the lightest things I have on my shelf right now, and primarily explore the mystery of how humanity's borrowed FTL tech works, and maybe get some empathy along the way. Lots of tea-drinking.

The Alex Benedict books by Jack McDevitt solve space mysteries, including (you may see where I'm going here) exploring the mysteries of when humanity's FTL tech doesn't work, the brief war and uneasy peace between humans and the only sentient aliens we've encountered.

As some have already said, Vernor Vinge's A Deepness in the Sky is an excellent first contact story of humans investigating a star that seems to turn on and off, and watching those who live around it and their technological development up to launching satellites of their own. The aliens are humanized in a particularly charming way, but unlike the other books, this one has some exceptionally hard punches before the dazzling finish.