In Paris, the public transportation system is divided into 8 zones (note that these transportation zones are not the same as arrondissements).  Zones 1 and 2 are in the center covering nearly every place in the city a tourist would want to go.  Further out is Versailles (zone 4), Parc Disneyland, the airports, and the suburbs.

Métro:  Designed for travel within Paris.  Serves tourists well for traveling within zones 1 and 2.  There are 14 major lines with 245 stations.  It is rare to not find a métro station within a 5-10 minute walk.  It is safe, clean and efficient.  Trains run frequently from 5:30 a.m. until about 1:15 a.m. on weeknights and about 1 ½ hours later on weekends and holidays.  The issue I have with the métro system is that it provides no perspective of location and the scenery is what would be expected when traveling in a hole in the ground.  There is probably more chance of petty crimes in the subway than in using the bus.  

RER train:  Best suited for transportation to/from outlying areas and suburbs as far as zone 8.  RER trains make limited intra-city stops within zones 1 & 2.  There are 5 RER lines.  Use the RER to go to Versailles, Parc Disneyland, and the airports.  Think of the RER as the commuter train that brings people in and out of Paris from the suburbs.

SNCF and TGV trains:  For inter-city travel and beyond.  For instance, we take a regular SNCF train from Paris to Vernon (Giverny) or to Bayeux (Normandy Invasion Beaches).  The high-speed, train-on-steroids TGV traveling at speeds up to 320kmh (198 mph) serves major cities and other parts of Europe.  Purchase tickets at a train station or an SNCF “boutique” located around Paris.  I find the boutique located near the entrance at the Musée d'Orsay RER train station to be least crowded and staffed by English-speaking agents providing courteous service.  Senior discounts are available on SNCF/TGV trains.

I have some reluctance about purchasing RER, SNCF and TGV tickets from the website RailEurope.Com.  They don’t always offer discounts (i.e., senior citizen, off-peak) that I can get when I visit an SNCF boutique or purchase at the train station.  They also don’t let online purchasers print tickets.  Instead, tickets are shipped to North America for a fee of about $15.   A better option is to purchase tickets on the website https://www.captaintrain.com (soon to become trainline.com).