Post processing VHS content

it would depend if the DVD footage was captured interlaced. They may have merged the fields and burned them merged.
avisynth qtgmc is the best free deinterlacer. also, you may have flicker in color, luma, artifacts, etc.
digital anarchy deflicker is good for deflicker. Any grain removal would have be to be done with a plugin like magic bullet denoiser.

you can try to fix white balance and exposure with lumetri, but all that will be limited to how they were first captured, which is mpeg2 low bitrate and unknown interlace fields.

Enlarging may be a final option. *you always enlarge after you color correct as enlarging blurs pixels.

Preserve upscale is bicubic in after effects, but you may need red giant instant 4k or similar plugin
for good upscale.

You can deinterlace, enlarge, in premiere, but you will lose more quality.
Avisynth is a pain, but you may end up with higher quality than basic premiere. Alternatively, you can shell out for a lot of plugins for restoration. It's all about time/money/quality.

That's really cool that you have stuff for family to recall growing up together, etc.

Normally those machines that made digital stuff from VHS tapes used AVI I think. The codec in your files ( in the VOB file ) would be a first step in figuring out how to handle editing the stuff. That has to do with your local storage and speed mostly ( and general computer specs to edit ).

It's easy enough to do the other stuff. Stay at SD dimensions. Maybe let it have black bars around it in a 720p timeline ? But don't upscale, that would be ugly.

Some answers:

Quickest and easiest improvement will come from a colour grade in Lumetri. Cameras of this era can be quite contrasty as seen in your example outside and have poor low light peformance indoors - both can be improved with a grade. 

Though don't expect wonders.

You could scale or crop your image slightly to get rid of the 'head switching' noise at the bottom of frame.

Deinterlacing would be nice as it will make the videos more 'online' friendly but the time and resources to do it really well are prohibitive. A simple deinterlace will throw away half your resolution (not good). Good to great deinterlacing would required a specialist deinterlacing plugin (From RE:Vision Effects for example) and these take significant render time.

Video noise reduction plugins can improve picture noise. Though again 'cost' and time!

Upscaling - not recommended in this instance.

So ... in light of what you are trying to achieve I would suggest;

Grade - yes, crop/scale for head switching noise - yes

and output to a universal format like MP4 so you can easily share. A datarate of about 6Mbit should be fine. Stay at SD resolution.