capturing analog video

Can you post your results? Perhaps your method will be better then mine. I do like the fact that Premiere Pro can make use of the Firewire DV converts. I find that helpful but others may not. 

Check the bitrate of the digitized files, try to be a tad higher on the export settings

Unless the elgato hardware explicitly says it supports 10 bit, you would have to assume its only h.264 8 bit. Exporting to a 10 bit codec would be a waste of space.

For ease of use, if premiere could natively import the h.264 files, you'd have to export out a lossless codec at full 4:4:4 RGB at 8 bit which would make large file sizes or try a high datarate 4:2:2 codec at slight quality loss. If you can edit and then export directly to dvd, that's another option as well. I'm a stickler for 0% loss of quality, even if I can't see it, my computer does, expecially when its trying to compress down to DVD-mpeg2, I want every last gigawatt of quality I can get. If you need offline clips stored losslessly, two codecs I like are quicktime png video and huffyuv video both full 4:4:4 RGB at 8 bit. or Png/Tiff image sequences with lzw lossless compression enabled.

As for the capturing at interlaced, that doesn't really make any sense for film. Hopefully, the capturing device is storing the fields in NTSC encoding as progressive fields, which means you don't need to deinterlace as both fields are captured at the same moment in time and thus frame independment and can simply be treated as a whole frame in time. (since deinterlacing would throw away half your resolution) If you had to deinterlace, use topaz as adobe just blends the fields. or compare with qtgmc deinterlacing but that works at YUY2(which may still be better)

If you could work the files entirely inside shutter encoder, you might be able to clip them without re-encoding. This would depend on if they were natively supported for lossless clipping.

As a final note, I would never capture anything analog into an interframe codec. interframe codecs cannot handle rapid motion and may create tearing artifacts. I'd only capture with intraframe 'I' frames.

The Elgato USB2 Video Capture device is pretty good, but it's really just meant for capturing the tape, trimming the head and the tail, and then exporting to MP4 (as I'm sure you've noticed).  It would be really great if Elgato added an Extract option for removing segments within the capture before exporting it to a stand alone MP4 file.  It's also important to note that the Elgato software de-interlaces the footage and crops for overscan resulting in a 480p29.97 clip.

You can import the captures that you've exported from Elgato directly into a Premiere Pro project.  Select one of the MP4s in the Project tab and then right-click to choose New Sequence from Clip.  Rename the resulting Sequence with a descriptive name and edit the clips as you'd like.  Repeat as needed for as many Sequences as needed.

When you're ready to export the Sequence, choose File > Export > Media.  In the Premiere Pro Export dialog box, you have a few options.  Setting the Format to H264 and the Preset to Match Source - High Bit Rate is probably the easiest, but you could use the Match Source - Adaptive High Bit Rate preset for a smaller file or any of the presets with "SD 480" in the name (but not "SD 480 Wide").  If you really want to keep the file size small, you could use HEVC H265 for a more efficient but less compatible file (that is, the file will be smaller but it'll only play on devices that support H265).

As far as quality goes, you are taking a H264 compression generation hit.  That is what it is unless you reacapture your Regular 8 tapes and VHS tapes with a higher end video capture device.  If you decide to take that route, look into a capture device that allows you to capture SD via S-Video/RCA to Apple ProRes422 LT.  I really like Blackmagic Design's products (https://www.blackmagicdesign.com/products/intensitypro4k) - just be sure to use their included Media Express software for the SD ProRes captures.  If you happen to have access to a Digital8 camcorder with DV pass-through, that's probably your best bet for recapturing the tapes via Premiere Pro's DV capture; however you'll need to have FireWire or Thunderbolt with the right adapters to FireWire.  If you go the route of recapturing your tapes to a higher end format, the Premiere Pro part is more or less the same:  Import the captured clips, right-click and choose New Sequence from Clip, etc., etc.

Have a look at this:

https://www.shutterencoder.com/en/

From what I see online the Elgato devices capture H.264 at 1.4 Mbits 640x480 or 640x360 resolution ...

so you are starting with a fairly low datarate and a resolution below standard SD - which is 720x486 (or 720x576 PAL).

So, yes I would suggest you edit your clips to what you want in Premiere Pro but make sure you use a higher datarate when exporting. You could export to (for example) 'Prores' to maintain the initially encoded quality. But this will create much larger file sizes and has limitations that may be an issue for you.

I think in your case you probably should export using H.264 at high quality. 

Encoding to H.264 will give you MP4 video clips that everyone can easily view, share, upload to YouTube etc.

(whereas Prores is not going to be a file you can easily share).

One of the reasons to go with higher datarates for you exports is; Stanadard Definition analogue formats like 8mm/VHS have a lot of video noise. And the cameras of that era were also noisy. Video noise compressed to lower datrates will look worse.

All that said - experiment!. Digitise your footage and test various export settings from Premiere Pro.

If you want to spend some money, there are some video noise reduction plugins for Premiere Pro that may improve the look of your footage.

Another option is the excellent Topaz Video Enhance AI application. It's a standalone app that can upres footage, denoise video and remove interlacing. It can also do 'in' & 'out' simple edits.