Recommend some Apps for my newly rooted Nexus 4

In My Humble Opinion
1

Now that my phone is rooted, any apps that require root you recommend?

2

-Tasker, of course.
-Any of the good file explorers (I like ES File Explorer and Solid Explorer)
-Titanium Backup, if you intend to do any flashing, as it makes restoring apps & settings painless

3

A firewall, many of them require root to be fully effective. I use Avast and it seems stable and unobtrusive. An extra bonus: you can block any given app from accessing the Internet.

4

The ones already mentioned and AdFree.