I second the advice to take the RER - However it runs to the Gare Du Nord. From there several metro lines connect, and it is an easy transfer. Make sure you have Euro's with you, as each ticket for the RER from the airport is about 9.00 Euros, and unless you have a credit card with the smart chip on the front, the cards won't work at the automatic ticket machines.
My wife and I have been to Paris a few times over the last few years, and we have stayed several times at the Timhotel St. Georges. It's located about 100 feet from a Metro stop, and it's a direct line from the Gare Du Nord. It's located in Pigalle, which was/is the red light district, but it's very safe, and mostly touristy these days. I think it runs about 120.00 Euros a night (it used to be 80.00, but they recently refurbished the hotel). Beware of any lower priced hotels, as you might not have a private bathroom. The Timhotel IMO is in a great location and is clean and safe.
The
hotel is well located, it's steps to the Metro, and Paris is very well connected with the Metro system. Also the Hotel is located at the bottom of the butte of Montmartre, cross the street and climb the hill and just wander the streets. There are great restaurants up the hill, and many are very affordable.
If you wanted to book an appartment, there are also some good deals on smaller apartments. Keep in mind that you're not in Paris to hang out in your room. You just need a place to leave your luggage and sleep. Check out VBRO dot com for a ton of options. My wife and I have book apartments in several cities around the world though there.
As for things to see? I second Versailles as a day trip, however I wouldn't suggest leaving the city. There is more than enough to see and do in Paris, that to travel to the south to a different city would be a bit of a waste. Another don't miss is the Cathedral in St. Denis. Take the metro north to the last stop and St. Denis, and follow the signs. It is the French equivalent to Westminster Abbey, and the artwork/crypts are second to none.
If you have any more questions or need any links/advice feel free to send me and email: andrew at internationalmetropolis dot com