How do you see yourself using the apps on your phone, and for what purpose?
If you watch YouTube a lot, Protube is a great 3rd party client.
Maybe invest in an ad blocker for a smoother web browsing experience. I use Crystal.
If you use Twitter, Tweetbot is an excellent twitter client.
Reeder if you subscribe to RSS feeds.
If you handle PDFS a great deal, PDF expert or Notability to better manage them.
Fantastical is a good replacement for the stock calendar app.
Next for tracking and recording expenses.
Scanner Pro if you routinely take scans of documents and receipts.
If you find yourself wishing for a better calculator app, consider Pcalc or Soulver.
Just off the top of my head.