SOme DVD players output 480i only, those that output 480p offer a manual choice between 480p and 480i.
Most display devices that accept 480i, 480p, 720p, etc. will autoselect which kind is coming in and fill the screen with it. Some display devices have more than one set of component video jacks, one set is for some scan rates, the other is for other scan rates.
Doubling 480p to 960p requires a different kind of doubler than doubling 480i to 480p. The latter process when done to the highest quality is referred to as de-interlacing rather than "just" doubling.
The 3-2 pulldown (repeating frames of 24 frame pre second film source) may be present in any of the scan rates 480i, 480p, 720p, and 1080i, and others too. All of the U.S. consumer video scan rates are about 60 frames per second if progressive or fields per second if interlaced so the 3-2 pattern is the same for all. The number of scan lines in each field or frame has nothin to do with 3-2 pulldown. I believe that 1080i was chosen for U.S. ATSC HDTV because it was already in use for Japanese HDTV. THe U.S. and Japanese 1080i video signals are transmitted over the air differnetly (digital vs. analog respectively) but when they get to the TV as component video they are the same (analog).
One thing often seen in poor quality de-interlacing is failure to preserve 3-2 pulldown when present in the interlaced input and instead even and odd fields that don't match get woven together for the progressive frames.
The process of converting the 480 scan lines of 480p to some other number (such as 720 for 720p or 540 for 1080i) is referred to as scaling. Scaling varies in quality from one scaler to another. Display devices that accept several scan rates usually have built in scalers. 480i should be de-interlaced before any (additionally needed) scaling is done. Otherwise it becomes treated as 240p and the quality is lower.
Video hints:
http://members.aol.com/ajaynejr/video.htm