You'll want Emprise, Book One of the Trigon Disunity
by Michael P. Kube-McDowell
The first book, "Emprise" was set in the early 21st century. Prince William is King of the British Empire after Charles and Diana were killed in an IRA attack.
Emprise (1985, ISBN 0-425-07763-2) : The world has been devastated by the Food and Fuel Wars turning once-powerful nations into loose groupings of isolated farming communities. Barter has replaced currency, and scientists — blamed for the world's misery — are burned at the stake. Hidden in the Idaho hills, astronomer Allen Chandliss struggles to maintain his primitive radio telescope, listening in secret for signs of the intelligent life, which may be the only hope to improve things on Earth. After seventeen years a repeating signal is received from Cassiopeia. He manages to send a message to a group of scientists in England. The race is on to decode the signal and then find the resources to respond to it...
Enigma (1986, ISBN 0-425-08767-0) : Set 150 years after the events of the first book, the 'aliens' turned out to be human and considered themselves to have been colonized from Earth in the distant past. The Unified Space Survey has been established to make contact with other remnants of the first colonization and to determined what happened to it...
Empery (1987, ISBN 0-425-09887-7): The catastrophe that befell the first human interstellar civilisation has been explained; destroyed by the alien Mizari from a black star in the Ursa Major cluster. But as the new galactic empire is formed the threat of the all-powerful Mizari remains...
Another enjoyable first-contact series is Juanita Coulson's Children of the Stars
Tomorrow's Heritage (Book 1) (1981)\
A futuristic, post-cataclysmic, sci-fi soap opera.
On an Earth whose population has been decimated and whose landscape has been forcibly altered by natural causes and the effects of humankind's weapons, political and national boundaries have been altered. The Saunder family has gained wealth and power due to the actions of the manipulative matriarch, and the three offspring are in positions of great power and responsibility. But the family has cracks that ultimately will risk tearing the family apart. And into this volatile mix comes news that an alien spacecraft is approaching Earth.
Hysteria, propaganda, deceit, betrayal and redemption. What every good stereotypical soap opera needs. Throw in some advanced technologies and alien visitation, and you've got a rather interesting result.
Outward Bound (Book 2) (1982)
Legacy of Earth (Book 3) (1989)
The Past of Forever (Book 4) (1989)
The four books follow the Saunders family with each book focused on a subsequent generation of the family. Book 1 is likewise set in late 20th or early 21st Century Earth. Book 2 establishes first contact with aliens and the development of FTL. Books 3 and 4 deal with the colonization of other planets and the expansion of humanity among a populated galaxy.