Camcorder Advice

I am looking to replace my old Sony DV camcorder. I don't need anything too fancy, but want to understand what HD means to me. I use it for home video,- holidays etc and the occasional school play that a create DVDs for the school to sell. Traditionally these go on DVD, and I intend to keep doing so for the time being at least.

So my questions are:
1080 or 1080p - will it make much difference now or in the future?

If I have a HD movie file and want to burn it to DVD I believe I have to convert the file first to the correct lower resolution? I'm guessing I can do this within the editing program by outputting it to the relevant file format?

Can I create better video quality on DVD's than with my DV camcorder, or is this only achieved using Blu-ray discs?

Thanks in advance.

EDIT: I've found that some camcorders allow you to select recording mode, but I guess it means you have to decide one way or the other from the outset of the recording. eg:

HD : Quality Records movies in high definition image quality (HD). Enjoy beautiful images on a big screen.
MP4 : Records movies in the MP4 format. This format is easy for playing back your movies on a smartphone, for uploading to a network or for uploading to the Web.
STD Quality : Records movies in standard definition image quality (STD). This is useful for saving your movies to a DVD.

If it helps, I am looking at the Sony PJ220 and the PJ200.