Ok, now that you got the arr. straightened out you want to hit the RATP site for a map of the metro. If you want to get around easily the metro is the best way. Bus is very nice but it takes a while to figure it out because there are so many lines. And the bus takes a long time. Metro is super fast.
In my humble opinion, it is most ergonomic to stay within walking distance from the yellow line #1. You will be able to reach most any point in Paris by changing trains only once. Plus, many attractions are on line number one anyway. Line #4 (purple) is also important.
The Chatelet station is the central station where most of the lines meet. It is huge and confusing but still practical.
Just to give you a rough idea of walking distances and times. Walking from the Hotel De Ville (almost the geographic center of Paris) to the Arc de Triomphe which is a straight shot, will take you probably just under one hour, if you only walk, no window shopping or checking out the sights.
To the Jardin du Luxembourg it will be around 20 minutes. To the Louvre around 15-20 minutes. To Bastille around 15, too.
Personally, I'd stay close to line 1. That means Marais (4arr), Chatelet (1arr), Bastille (11arr) or Champs (8arr.) Of these, the Marais is the most charming and has tons of boutique hotels, bars, restaurants and shops. It is the SoHo of Paris.
On the other side of the Seine you have St. Germain. Very chic, very expensive and also very charming. Not as practical though as the Marais for traffic connections.
Till