Two issues here.
First, your DVD is standard definition. There's just no way to make that look as good as the high definition original. So...I'm afraid the only solutions here are to lower your expectations, or simply build a Blu-ray.
Second, because of the Pixel Aspect Ratio used for widescreen standard definition material, there will be very small black bars when downressing HD media. Most TVs will not show those bars due to overscan, so it's probably something you can just ignore.
I would have to ask why you are exporting to H.264, if intending to make a DVD? Then you are creating an extra compression step in the process, taking an already compressed file and then recompressing to MPEG-2 for DVD.
From Premiere, use Adobe Media Encoder and choose an "MPEG-2 for DVD" format, with "NTSC Widescreen High Quality" preset (or PAL, as applicable). If working with Progressive source footage, then of course choose a Progressive preset.
Set the data rate according to program length, with your choice of CBR or VBR, and be sure to check the "Maximum Render Quality" button at the bottom, as this helps with the downscale quality. Rule of thumb is 560/minutes=data rate, not to exceed 8 for video stream. Maybe round result down just a bit for safety margin.
In Encore, use "Import as Timeline" and import the resulting .m2v video and .wav audio files. Any chapter marks in Premiere will also come in automatically.
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Another way is to use the Adobe dynamic link in Premiere Pro, by going to file, then Adobe Dynamic link, send to Encore. Encore will be launched automatically and your sequence will be ready to be linked to menus and assets for building. If you have hardware MPE, then you may not need to check the Maximum Render Quality, saving yourself hours of encoding.