Below are some NRass members suggestions on how to start using this suite.

- simAd_Nraas simAd_Nraas
For someone just starting to use NRaas mods, the whole bunch of them seems daunting. However, once you start using one or two and get a
feel for what the others may do, you may end up downloading a lot of them. They're modular and most can be used standalone.
You'll find a brief overview of what every mod does here: http://nraas.wikispaces.com/NRaas+Industries+Home+Continued#The%20Mods

Please be aware that all mods on this site should be updated to the latest patch available. Check Update History to stay posted on the latest status.
I myself started with Master Controller because I wanted to add some traits to a Sim. It was all downhill from there. StoryProgression was actually
one of the latest, because it is a very involved mod with many settings, and perhaps not suited for a beginner.

- brappl brappl

A good way to start is to become familiar with the NRaas Wiki itself by exploring the different sections to become more familiar with the site. Take a few minutes to read The Home Page
That way when you do have a question or problem, you will know where to look for an answer or additional help. Just knowing there is help available is reassuring!
I now have most of the NRass mods in my game. In addition to Overwatch and Error Trap these are a few I used to get started:
Master Controller
Master Controller Cheats
DebugEnabler
Register
Traffic
Saver
Base Module for Story Progression - You really do not need to make adjustments to the base module if you choose not to. It's a good way to get started with the Mod and you can gradually add other modules as you become more experienced.

For Beginners, and perhaps those who are not all that new to the NRaas Mods, Story Progression is HUGE so WHERE DO I START is a must read!

- J4Ks J4Ks
Also, one other page you might be interested in is "Other Mods FAQs" -
If you're not sure which mods are the best usage for you. You might want to read upon this first FAQ which mods and
The General FAQ's section Listings
Try a combination of some of the mods listed over there and see how the mods interaction works for you to start with, so you can get a hang of it's inner workings.
From there on, if you have any questions, how to do something or if something is possible with these mods, just pop by and ask it here in the Chatterbox.

Other than that I can only recommend you to have these two mods installed at all times:
- ErrorTrap catches corrupt data from your saved files
- Overwatch cleans up your game from obsolete in-game objects and resetting stuck sims (has adjustable settings, but you can leave it on its default)
These two mods works in the background, and once in a while, pop up notifications on the current tasks they're doing in game.

- igazor igazor
It is helpful to note that each mod has its own comprehensive Interactions page. For example:
Master Controller Interactions
You might want to browse that page first, not to take it all in, but to get a feel for how the commands are organized.
Then return to your game and click on a Sim (or Household, Town Hall, etc.), pull up the NRaas > MC commands, and note that they map onto the same hierarchy as the Interactions page.
THEN, start reading about what the more interesting commands to you actually do.
As others have stated, StoryProgression is the most complex and it's probably a good idea to set that one aside until you get more of a handle on the others.