Sounds like you have the option to go Progressive the whole way. If so I’d just do that.
Basically progressive scan has a more, well, “film-like” look if you will. That was originally what all of the hype was about 10 years ago or so - gee, has it been that long? That was about when it started to hit the market more broadly in cameras, though I am sure it had been around a lot longer.
One of the main advantages of 24p is you can take film footage and transfer it over and remain more true to a projected look. That is because each frame is scanned once (similar to a camera and projector) rather than two times (interlaced).
The interlaced look is what has been associated with TV footage. A more “video - like” look.
Personally, I have always been able to tell the difference between the two even when shown on an NTSC interlaced monitor. I have also had the great opportunity to see the film I shot (that we edited in Progressive) projected at the Archlight Cinerama dome. The consensus was that we had transferred to film, when in fact it was just a very good video projector projecting the progressive tape in Progressive on the screen.
As noted above there are some technical issues to consider. However for the most part, I think you’ll like the end result better if you shoot in 1080p and then render in progressive.
Just make sure in Premier, to see to it that each clip is set to Progressive, (not sure how Premier does this, just check them to make sure is all I am saying) and the project is also set to Progressive. And when you render out any composites or final edits from Premier you select Progressive. Same would be true I expect with AE. Sorry I use Vegas. But the basic idea is still true. Make sure all your settings are progressive as you go down the pipeline - including the MPeg files you render for the DVD output.
If you change your mind later you can always convert clips to interlace. NLEs are pretty good with this stuff these days, so there should not be any problems.
As a technical note: I had done quite a bit of experiments before shooting. And in the end I shot in interlaced but when I did the editing, I converted the clips to Progressive. But that was an old camera. These days you can just shoot progressive with most real nice cameras that have true progressive. But it is a good idea to do tests before you get to the set and see what works best in your situation.
The bottom line is you always have options to convert in post. You should shoot based on what looks best or works best in tests you do beforehand.