My favorites of this type are indeed the Vernor Vinge you reference and
Arthur C. Clark's - Rendezvous With Rama (I'm sure that's ebooked) Hugo Award
Frederik Pohl's - Gateway, Hugo Award
David Brin's - Startide Rising (no idea if ebooked) Hugo Award
and
C.J. Cherryh's - The Pride of Chanur (ebook version on her website I think) Hugo nominee
edit: I'm wrong, The Pride of Chanur is still in the publisher's domain and not available as an ebook. What it's about is: from an alien species point of view, first contact with the (Earth Company part of the Company/Alliance/Union universe) humans. Just tremendous

-- If you pursue it in paper form, be aware that Pride is a standalone book, the next 3 - Venture, Kif and Homecoming are really one long book. Someone published Pride, Venture and Kif together in an omnibus without her approval which left the story hanging practically in mid sentence, back around 2000. Be wary of that paperback. Personally, I like the high quality Phantasia Press imprint of the Chanur books which can be had for like 10-15 bucks on Ebay or abebooks.com. But you can also find 'em for a buck somewhere in paperback.
On her website are "Heavy Time" and "Hellburner", the first two Company Wars books which are somewhat related later to the Chanur books. Heavy Time is one of my favorite books by her and while not "alien first contact", it is the beginning of a long, related, group of standalone books about contact between 1) Earth (Company), 2) the Merchanter Alliance and 3) Union, those original colonists who are now so far away from Earth they have become a separate .... culture in the galaxy.