As the data and destiny expansion did not come with any deck lists I was wondering if anyone had tips for how to construct decks for these new runners Apex, Adam and Sunny Lebeau
Yes! Instead of answering here, I'll link you to netrunnerdb. It is one of several sites that provide tools for building and sharing Android: Netrunner decks. If you are looking for ideas around a specific card or group of cards, you can do a query like this one to see decks other people have built that include that card.