Paris Visite is a more expensive tourist thing, with a discount voucher book for museums, etc...
I would suggest you to get what the locals use when they need a day of unlimited travel.
It is called the Mobilis. Costs less than the Paris Visite and much less advertised; its counterpart is that you cannot use it on Orlyval. It is valid on other public-transport links to the airports (Orlybus, Roissybus, RER B, …) since 2018.
On week-end days, if you're less than 26 years old, there is also the cheaper Ticket Jeunes week-end. This ticket is valid in the specified zones for one day (until midnight, not until end of service), on a Saturday, Sunday or public holiday. Note that unlike Mobilis, this ticket is not valid on the direct airport links (Orlyval, Orlybus, Roissybus, RER B to Roissy).
Also, if you stay for the week, you may consider getting a Navigo weekly pass. Weeks are forced from Monday to Sunday. It involves getting a €5 anonymous card and sticking a photo on it.
Choose your zones wisely : there are no extension tickets available yet. For example : if you got zones 1-2 and you wish to visit Versailles in zone 4, you'll have to pay a ticket for the full zone 1 to zone 4 trip, or get off at the last zone 2 station and buy the "remaining" portion there, which is rather inconvenient. When buying single-trip tickets to use Transilien/RER outside of Paris, you have to request the exact station name you are targeting and there is no fare adjustment; you may be fined if you go further or change routes and an inspector comes.
Once you get your day ticket or weekly pass, the rule is very simple : travel is unlimited within the zones you bought. Metro, bus, Transilien/"train de banlieue" (commuter train ending at main stations), RER (commuter train crossing the city in tunnels, more like metro), tramway, night bus, all is included.
The metro has a very fine network of stations; anywhere you get lost in the city, you will always be able to walk to a station in a few minutes.
The RER lines come to your advantage as they cover larger distances between stops, and run faster.
A note about accessibility :
Most RER stations have escalators and lifts, as well as Metro line 14.
Other, older metro lines mostly have stairs. In big stations you may find some escalators. Most Paris Metro stations are below the surface and involve climbing the equivalent of 2-3 floors to get out, unlike the very deep London tube. There also are aerial stations on lines 2 and 6.
Consider taking the bus too. Get a bus map; there are many routes crisscrossing around Paris. Bus is running on the street, saving the need to use stairs; beware of traffic and rush hour anyway.
If you want to ride a tourist bus, there are two main companies who operate open-top double-decker buses : OpenTour (green/yellow vehicles) and Les Cars Rouges (red vehicles). They only sell unlimited passes at tourist prices i.e. much more than the average transit option.