What tools do you recommend to profile Rails apps?
New Relic offers Rails profiling including a free 'Lite' version.
How can I profile a Rails app in its entirety, not just controllers?
The well know ruby-prof may help you. The config.ru file of your rails app will give you some hints on running the app manually.
For other alternatives take a look at this question.
How to profile a Rails request with details?
It sounds like you're looking for rack-perftools_profiler. I've used this for exactly what you're describing and it works well.
Pointers to learn how to use DTrace
I did a 35 min video and showed some DTrace starter examples that you can find here: http://cocoasamurai.blogspot.com/2008/05/dtrace-for-cocoa-developers.html which were intended for introducing DTrace to Cocoa Developers, but it can work for anybody really
Rails 4 memory profiling
Oink is something I use with Rails 4.
Oink adds memory and active record instantiation information to rails
log during runtime and provides an executable to help digest the
Given a minimum threshold and a metric (memory or active record
instantiation), the oink executable reports:
The top ten single requests which exceeded the threshold for the
metric, ordered by the request which exceeded the threshold the most
The number of times each action exceeded the threshold for the metric,
ordered by the action which exceeded the threshold the most
(in verbose mode) The log lines produced by requests which exceeded