Your Mark I lens should be fine with the 1.4X Kenko Pro 300 DG or DGX... I can't show examples because I don't have that particular teleconverter myself, though I have the lens. Instead I use the Canon 1.4X II, but even that rarely sees use on my 70-200 simply because I have two 300mm lenses, and nearly always have one or the other of them on hand to use. People who have the Kenko say it matches the Canon 1.4X II for image quality. When you've got an itch...
I would not be so quick to use any 2X on that zoom. I've done some test shots with the Canon 2X II on it and haven't been happy with the results. I'd rather use a 300mm with a 1.4X.
In general 2X don't work particularly well with zooms. An exception... The new 70-200/2.8 IS Mark II appears to work quite well with the Canon 2X Mark III. And there are probably some other rare exceptions... For example the Sigma 120-300 OS appears to work pretty well with 2X. But, generally I wouldn't expect a 2X to work well on a zoom.
Be careful though, there is also another, somewhat cheaper Kenko... "1.4X MC4" or something like that... that's not quite as good.
These might not help because they are Canon 1.4X II on 300mm (a combo I use much more often):
EF 300mm f4 IS lens with EF 1.4X II TC at f8. EOS 5D Mark II camera at ISO 1600, 1/250 shutter speed. Handheld or monopod, available light. Young black tail mule deer (m)
EF 300mm f4 IS lens with EF 1.4X II TC at f5.6. EOS 5D Mark II camera at ISO 1600, 1/400 shutter speed. Handheld or monopod, available light.
In summary, from all I've seen and heard and experienced myself I would have little concern about using the following combos:
EF 70-200/2.8 IS "Mark I" with Canon 1.4X II or III, or Kenko 300 DG/DGX 1.4X.
EF 70-200/2.8 IS Mark II with Canon 1.4X II or III, or Kenko 300 DG/DGX 1.4X.
EF 70-200/2.8 IS Mark II with Canon 2X Mark III.