Of course it depends on how you use it. One of the first I would install is Android Device Locator that will let you find your phone, ring it or remote wipe. Google apps are essential as many things are or can be tied into your Google account (Play store, maps, calendar, google docs, sheets, chrome, Gmail, Hangouts, Keep, You Tube, etc. Most are probably installed by default).
For basic clock/weather widgets on the home page try Beautiful Widgets or HD widgets. If you want to customize your experience try Nova Launcher that customizes app drawer, dock, screen, etc. A good file manager is handy (File Expert HD, ES File Explorer). Pushbullet will allow you to transfer files easy from PC<>phone, and get notifications on PC.
Look for some of the same apps you used on apple if you have favorites. Other general apps I like: Adobe Reader, Amazon (for access to shopping or prime account), Amazon Kindle, Amazon Appstore (for access to free apps and deals), Barcode scanner, Bible (from lifechurch.tv), Facebook, Messenger (Facebook), Flashlight, IMDB, Dropbox, Instagram, Pandora, Pinterest, Soundhound or Shazam, The Weather Channel, Twitter, QuickPic (better than default Gallary or photos app), Wikipedia, Feedly (if you follow a lot of websites/blogs), Those are some of the basics.
Some of my less common favorites: AFWall+ (for controlling what apps can use my limited data plan), Amazon music (for playing free music through Amazon Prime), BSPlayer Free (can play most video file formats), Xfinity apps if you have Comcast (Connect, Xfinitiy Wifi, X1 remote, xfinity tv), Droid48 (because I'm an HP calculator Geek), Goodreads to track books read, Keyring for loyalty cards), NIV Bible from Tecarta, Packing list full (for keeping packing lists for trips), Remember Me (for Bible verse memory), ESPN, Tapatalk (for forums), ToMarket Pro (for grocery shopping list), TV Guide, TV Show Favs (for tracking what episodes watched), Zillow & Realtor.com (for real estate).
And of course you can't forget the Android Central app! That give you a start. Hope that helps.